Topic Quiz • 150 questions • 40 seconds per question.
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What is the sum of the first (10) natural numbers?
C. (55)
सूत्र (S_n=\frac{n(n+1)}{2}) से \(S_{10}=\frac{10\cdot11}{2}=55\)। परीक्षा में (n) की जगह सही संख्या रखें। / Using (S_n=\frac{n(n+1)}{2}), \(S_{10}=\frac{10\cdot11}{2}=55\). In exams, put the correct value of (n).
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Find the sum of the first (20) natural numbers.
B. (210)
\(S_{20}=\frac{20\cdot21}{2}=210\)। पहले (20) को (2) से काटना गणना आसान करता है। / \(S_{20}=\frac{20\cdot21}{2}=210\). Cancelling (20) by (2) first makes calculation easy.
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If (S_n=\frac{n(n+1)}{2}), what is \(S_{15}\)?
D. (120)
\(S_{15}=\frac{15\cdot16}{2}=120\)। गुणा करने से पहले (16) को (2) से भाग दें। / \(S_{15}=\frac{15\cdot16}{2}=120\). Divide (16) by (2) before multiplying.
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What is the value of \(1+2+3+\cdots+25\)?
A. (325)
पहले (25) प्राकृतिक संख्याओं का योग \(\frac{25\cdot26}{2}=325\) है। लंबे जोड़ में सूत्र समय बचाता है। / The sum of the first (25) natural numbers is \(\frac{25\cdot26}{2}=325\). The formula saves time in long addition.
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Which is the sum of the first (30) natural numbers?
D. (465)
\(S_{30}=\frac{30\cdot31}{2}=465\)। (30) को पहले (2) से भाग देने पर \(15\cdot31\) मिलता है। / \(S_{30}=\frac{30\cdot31}{2}=465\). Dividing (30) by (2) first gives \(15\cdot31\).
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How much is the sum of the first (12) natural numbers?
B. (78)
\(S_{12}=\frac{12\cdot13}{2}=78\)। सूत्र में (n=12) सीधे रखें। / \(S_{12}=\frac{12\cdot13}{2}=78\). Put (n=12) directly in the formula.
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Which is the correct formula for the sum of the first (n) natural numbers?
C. (\frac{n(n+1)}{2})
पहले (n) प्राकृतिक संख्याओं का योग (\frac{n(n+1)}{2}) होता है। सूत्र याद रखना इस अध्याय की मुख्य कुंजी है। / The sum of the first (n) natural numbers is (\frac{n(n+1)}{2}). Remembering this formula is the main key for this chapter.
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What is the sum of \(1+2+3+\cdots+50\)?
B. (1275)
\(S_{50}=\frac{50\cdot51}{2}=1275\)। पहले (50) को आधा करें फिर (51) से गुणा करें। / \(S_{50}=\frac{50\cdot51}{2}=1275\). Halve (50) first and then multiply by (51).
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Find the sum of the first (5) natural numbers.
C. (15)
(1+2+3+4+5=15)। छोटे (n) के लिए सीधे जोड़कर भी जांच सकते हैं। / (1+2+3+4+5=15). For small (n), you can also check by direct addition.
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What will be the sum of the first (8) natural numbers?
A. (36)
\(S_8=\frac{8\cdot9}{2}=36\)। (8) को (2) से भाग देकर \(4\cdot9\) करें। / \(S_8=\frac{8\cdot9}{2}=36\). Divide (8) by (2) and calculate \(4\cdot9\).
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Which is the sum of the first (18) natural numbers?
B. (171)
\(S_{18}=\frac{18\cdot19}{2}=171\)। आधा करके \(9\cdot19\) लिखना आसान है। / \(S_{18}=\frac{18\cdot19}{2}=171\). It is easy to write it as \(9\cdot19\).
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If the sum of the first (n) natural numbers is (120), what is (n)?
C. (15)
\(\frac{15\cdot16}{2}=120\), इसलिए (n=15)। ऐसे प्रश्नों में विकल्पों को सूत्र में रखकर जांचें। / \(\frac{15\cdot16}{2}=120\), so (n=15). In such questions, test the options in the formula.
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How much is the sum of the first (40) natural numbers?
C. (820)
\(S_{40}=\frac{40\cdot41}{2}=820\)। (40) का आधा (20) लेकर \(20\cdot41\) करें। / \(S_{40}=\frac{40\cdot41}{2}=820\). Take half of (40) as (20) and calculate \(20\cdot41\).
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What will be the value of \(1+2+3+\cdots+100\)?
B. (5050)
\(S_{100}=\frac{100\cdot101}{2}=5050\)। बड़े योग में सूत्र सीधे उपयोग करें। / \(S_{100}=\frac{100\cdot101}{2}=5050\). Use the formula directly for large sums.
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What is the sum of the first (7) natural numbers?
D. (28)
\(S_7=\frac{7\cdot8}{2}=28\)। विषम (n) में अगले सम संख्या को पहले (2) से भाग दें। / \(S_7=\frac{7\cdot8}{2}=28\). For odd (n), divide the next even number by (2) first.
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Find the sum of the first (9) natural numbers.
A. (45)
\(S_9=\frac{9\cdot10}{2}=45\)। (10) को (2) से भाग देकर \(9\cdot5\) करें। / \(S_9=\frac{9\cdot10}{2}=45\). Divide (10) by (2) and calculate \(9\cdot5\).
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If (S_n=\frac{n(n+1)}{2}), what is \(S_6\)?
B. (21)
\(S_6=\frac{6\cdot7}{2}=21\)। सूत्र में (n=6) सही ढंग से रखें। / \(S_6=\frac{6\cdot7}{2}=21\). Put (n=6) correctly in the formula.
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How much will be the sum of the first (14) natural numbers?
C. (105)
\(S_{14}=\frac{14\cdot15}{2}=105\)। पहले (14) को (2) से भाग देकर \(7\cdot15\) करें। / \(S_{14}=\frac{14\cdot15}{2}=105\). Divide (14) by (2) first and calculate \(7\cdot15\).
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What is the sum of the first (11) natural numbers?
B. (66)
\(S_{11}=\frac{11\cdot12}{2}=66\)। (12) का आधा (6) लेकर \(11\cdot6\) करें। / \(S_{11}=\frac{11\cdot12}{2}=66\). Take half of (12) as (6) and calculate \(11\cdot6\).
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If the sum of the first (n) natural numbers is (55), what will (n) be?
C. (10)
\(\frac{10\cdot11}{2}=55\), इसलिए (n=10)। विकल्पों को जल्दी जांचना आसान तरीका है। / \(\frac{10\cdot11}{2}=55\), so (n=10). Testing options quickly is an easy method.
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Which is the sum of the first (16) natural numbers?
D. (136)
\(S_{16}=\frac{16\cdot17}{2}=136\)। (16) को आधा करके \(8\cdot17\) करें। / \(S_{16}=\frac{16\cdot17}{2}=136\). Halve (16) and calculate \(8\cdot17\).
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Which is correctly written for the sum \(1+2+3+\cdots+n\)?
B. (\frac{n(n+1)}{2})
(1+2+3+\cdots+n=\frac{n(n+1)}{2}) होता है। यह मूल सूत्र हर प्रश्न में काम आता है। / (1+2+3+\cdots+n=\frac{n(n+1)}{2}). This basic formula is useful in every question.
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Find the sum of the first (13) natural numbers.
C. (91)
\(S_{13}=\frac{13\cdot14}{2}=91\)। (14) का आधा (7) लेकर \(13\cdot7\) करें। / \(S_{13}=\frac{13\cdot14}{2}=91\). Take half of (14) as (7) and calculate \(13\cdot7\).
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How much is the sum of the first (4) natural numbers?
C. (10)
(1+2+3+4=10)। छोटे योग में सीधे जोड़कर उत्तर जांच सकते हैं। / (1+2+3+4=10). In small sums, you can check the answer by direct addition.
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What will be the sum of the first (22) natural numbers?
A. (253)
\(S_{22}=\frac{22\cdot23}{2}=253\)। (22) का आधा (11) लेकर \(11\cdot23\) करें। / \(S_{22}=\frac{22\cdot23}{2}=253\). Take half of (22) as (11) and calculate \(11\cdot23\).
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If \(S_n=465\), what is the value of (n)?
C. (30)
\(\frac{30\cdot31}{2}=465\), इसलिए (n=30)। विकल्पों में से सूत्र से मिलान करें। / \(\frac{30\cdot31}{2}=465\), so (n=30). Match the options with the formula.
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How much is the sum of the first (24) natural numbers?
C. (300)
\(S_{24}=\frac{24\cdot25}{2}=300\)। पहले (24) को आधा करके \(12\cdot25\) करें। / \(S_{24}=\frac{24\cdot25}{2}=300\). First halve (24) and calculate \(12\cdot25\).
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What is the sum of the first (3) natural numbers?
C. (6)
(1+2+3=6)। शुरुआती पदों में सीधे जोड़ना सबसे सरल है। / (1+2+3=6). For the first few terms, direct addition is simplest.
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Find the sum of the first (60) natural numbers.
A. (1830)
\(S_{60}=\frac{60\cdot61}{2}=1830\)। बड़े (n) में सूत्र सीधे उपयोग करें। / \(S_{60}=\frac{60\cdot61}{2}=1830\). Use the formula directly for large (n).
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If the sum of the first (n) natural numbers is (210), what is (n)?
C. (20)
\(\frac{20\cdot21}{2}=210\), इसलिए (n=20)। सही (n) के लिए विकल्पों को सूत्र में रखें। / \(\frac{20\cdot21}{2}=210\), so (n=20). Put the options in the formula to find the correct (n).
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What is the sum of the first (17) natural numbers?
C. (153)
\(S_{17}=\frac{17\cdot18}{2}=153\)। (18) को (2) से भाग देकर \(17\cdot9\) करें। / \(S_{17}=\frac{17\cdot18}{2}=153\). Divide (18) by (2) and calculate \(17\cdot9\).
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What is the value of \(1+2+3+\cdots+19\)?
B. (190)
\(S_{19}=\frac{19\cdot20}{2}=190\)। पहले (20) का आधा (10) करें। / \(S_{19}=\frac{19\cdot20}{2}=190\). First halve (20) to get (10).
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Which is the sum of the first (2) natural numbers?
C. (3)
(1+2=3)। प्राकृतिक संख्याएं (1) से शुरू होती हैं। / (1+2=3). Natural numbers start from (1).
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What will be the sum of the first (26) natural numbers?
C. (351)
\(S_{26}=\frac{26\cdot27}{2}=351\)। (26) को (2) से भाग देकर \(13\cdot27\) करें। / \(S_{26}=\frac{26\cdot27}{2}=351\). Divide (26) by (2) and calculate \(13\cdot27\).
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If \(S_n=78\), what will be the value of (n)?
C. (12)
\(\frac{12\cdot13}{2}=78\), इसलिए (n=12)। उत्तर को सूत्र से जांचना जरूरी है। / \(\frac{12\cdot13}{2}=78\), so (n=12). It is important to verify the answer with the formula.
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How much is the sum of the first (35) natural numbers?
C. (630)
\(S_{35}=\frac{35\cdot36}{2}=630\)। (36) को आधा कर \(18\cdot35\) करें। / \(S_{35}=\frac{35\cdot36}{2}=630\). Halve (36) and calculate \(18\cdot35\).
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A student added all natural numbers from (1) to (10). What sum will he get?
A. (55)
(1) से (10) तक का योग \(S_{10}=55\) है। ऐसी स्थिति में पहले और अंतिम संख्या से (n) पहचानें। / The sum from (1) to (10) is \(S_{10}=55\). In such cases, identify (n) from the last number.
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What is the sum of the first (45) natural numbers?
B. (1035)
\(S_{45}=\frac{45\cdot46}{2}=1035\)। (46) का आधा (23) लेकर \(45\cdot23\) करें। / \(S_{45}=\frac{45\cdot46}{2}=1035\). Take half of (46) as (23) and calculate \(45\cdot23\).
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If \(S_n=325\), what will (n) be?
C. (25)
\(\frac{25\cdot26}{2}=325\), इसलिए (n=25)। विकल्पों को सूत्र से जांचें। / \(\frac{25\cdot26}{2}=325\), so (n=25). Check the options using the formula.
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How much will be the sum of the first (28) natural numbers?
A. (406)
\(S_{28}=\frac{28\cdot29}{2}=406\)। (28) का आधा (14) लेकर \(14\cdot29\) करें। / \(S_{28}=\frac{28\cdot29}{2}=406\). Take half of (28) as (14) and calculate \(14\cdot29\).
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Find the sum of the first (32) natural numbers.
C. (528)
\(S_{32}=\frac{32\cdot33}{2}=528\)। (32) का आधा (16) लेकर \(16\cdot33\) करें। / \(S_{32}=\frac{32\cdot33}{2}=528\). Take half of (32) as (16) and calculate \(16\cdot33\).
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What is the sum of the first (1) natural number?
B. (1)
पहली प्राकृतिक संख्या (1) है, इसलिए योग (1) है। प्राकृतिक संख्याएं (1) से शुरू होती हैं। / The first natural number is (1), so the sum is (1). Natural numbers start from (1).
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What is the sum of \(1+2+3+\cdots+75\)?
C. (2850)
\(S_{75}=\frac{75\cdot76}{2}=2850\)। (76) का आधा (38) लेकर \(75\cdot38\) करें। / \(S_{75}=\frac{75\cdot76}{2}=2850\). Take half of (76) as (38) and calculate \(75\cdot38\).
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If the sum of the first (n) natural numbers is (36), what is (n)?
C. (8)
\(\frac{8\cdot9}{2}=36\), इसलिए (n=8)। विकल्प को सूत्र में रखकर जल्दी जांचें। / \(\frac{8\cdot9}{2}=36\), so (n=8). Quickly check the option in the formula.
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Which is the sum of the first (23) natural numbers?
B. (276)
\(S_{23}=\frac{23\cdot24}{2}=276\)। (24) का आधा (12) लेकर \(23\cdot12\) करें। / \(S_{23}=\frac{23\cdot24}{2}=276\). Take half of (24) as (12) and calculate \(23\cdot12\).
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What is the sum of the first (27) natural numbers?
B. (378)
\(S_{27}=\frac{27\cdot28}{2}=378\)। (28) का आधा (14) लेकर \(27\cdot14\) करें। / \(S_{27}=\frac{27\cdot28}{2}=378\). Take half of (28) as (14) and calculate \(27\cdot14\).
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A teacher asked to add numbers from (1) to (15). What is the correct sum?
C. (120)
(1) से (15) तक का योग \(S_{15}=120\) है। अंतिम संख्या ही (n) होती है। / The sum from (1) to (15) is \(S_{15}=120\). The last number is (n).
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How much is the sum of the first (55) natural numbers?
A. (1540)
\(S_{55}=\frac{55\cdot56}{2}=1540\)। (56) का आधा (28) लेकर \(55\cdot28\) करें। / \(S_{55}=\frac{55\cdot56}{2}=1540\). Take half of (56) as (28) and calculate \(55\cdot28\).
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If \(S_n=91\), what is the correct value of (n)?
C. (13)
\(\frac{13\cdot14}{2}=91\), इसलिए (n=13)। उत्तर को सूत्र से अवश्य सत्यापित करें। / \(\frac{13\cdot14}{2}=91\), so (n=13). Always verify the answer with the formula.
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What will be the sum of the first (36) natural numbers?
C. (666)
\(S_{36}=\frac{36\cdot37}{2}=666\)। (36) को आधा कर \(18\cdot37\) करें। / \(S_{36}=\frac{36\cdot37}{2}=666\). Halve (36) and calculate \(18\cdot37\).
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Find the sum of the first (15) natural numbers.
C. (120)
\(S_{15}=\frac{15\times16}{2}=120\) होता है। गुणा करने से पहले (2) से काटना आसान रहता है। / \(S_{15}=\frac{15\times16}{2}=120\). Cancelling by (2) before multiplication makes it easier.
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What is the value of \(1+2+3+\cdots+20\)?
A. (210)
यह पहली (20) प्राकृतिक संख्याओं का योग है इसलिए \(S_{20}=210\)। बिंदुओं वाला \(\cdots\) क्रम जारी रहने का संकेत देता है। / This is the sum of the first (20) natural numbers, so \(S_{20}=210\). The dots \(\cdots\) show that the sequence continues.
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Which is the sum of the first (7) natural numbers?
D. (28)
(1+2+3+4+5+6+7=28) होता है। छोटे (n) में सीधे जोड़ना भी उपयोगी है। / (1+2+3+4+5+6+7=28). For small (n), direct addition is also useful.
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If the sum of the first (n) natural numbers is (45), what is (n)?
B. (9)
\(S_9=\frac{9\times10}{2}=45\) इसलिए (n=9)। ऐसे प्रश्नों में विकल्पों को सूत्र में रखकर जांचना तेज होता है। / \(S_9=\frac{9\times10}{2}=45\), so (n=9). In such questions, checking options in the formula is fast.
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What will be the sum of the first (12) natural numbers?
C. (78)
\(S_{12}=\frac{12\times13}{2}=78\) है। पहले (12) को (2) से भाग देने पर गणना सरल हो जाती है। / \(S_{12}=\frac{12\times13}{2}=78\). Dividing (12) by (2) first simplifies the calculation.
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A student adds the first (18) natural numbers. What is the correct sum?
A. (171)
\(S_{18}=\frac{18\times19}{2}=171\) होता है। प्राकृतिक संख्याएँ (1) से शुरू होती हैं। / \(S_{18}=\frac{18\times19}{2}=171\). Natural numbers start from (1).
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Find the sum of all natural numbers from (1) to (25).
B. (325)
\(S_{25}=\frac{25\times26}{2}=325\) है। (1) से (25) तक का अर्थ पहली (25) प्राकृतिक संख्याएँ है। / \(S_{25}=\frac{25\times26}{2}=325\). From (1) to (25) means the first (25) natural numbers.
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What is the sum of the first (5) natural numbers?
C. (15)
(1+2+3+4+5=15) होता है। छोटे प्रश्नों में भी क्रम (1) से ही शुरू करें। / (1+2+3+4+5=15). Even in small questions, start the sequence from (1).
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For which (n) will the sum of the first (n) natural numbers be (66)?
D. (12)
\(S_{11}=66\) क्योंकि \(\frac{11\times12}{2}=66\)। विकल्पों में (n) रखकर मिलान करें। / \(S_{11}=66\) because \(\frac{11\times12}{2}=66\). Substitute the options for (n) and match.
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If (S_n=\frac{n(n+1)}{2}), what is the value of \(S_6\)?
B. (21)
\(S_6=\frac{6\times7}{2}=21\) है। सूत्र में (n) की जगह दी गई संख्या रखें। / \(S_6=\frac{6\times7}{2}=21\). Put the given number in place of (n) in the formula.
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Choose the sum of the first (30) natural numbers.
D. (465)
\(S_{30}=\frac{30\times31}{2}=465\) है। (30) को आधा करके \(15\times31\) करें। / \(S_{30}=\frac{30\times31}{2}=465\). Halve (30) and calculate \(15\times31\).
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What is the sum of \(1+2+3+\cdots+14\)?
A. (105)
यह \(S_{14}\) है और \(S_{14}=\frac{14\times15}{2}=105\)। अंतिम पद (14) ही (n) है। / This is \(S_{14}\), and \(S_{14}=\frac{14\times15}{2}=105\). The last term (14) is (n).
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The sum of the first (9) natural numbers is equal to which value?
C. (45)
\(S_9=\frac{9\times10}{2}=45\) होता है। याद रखें (9) तक जोड़ने में (10) गुणक आता है। / \(S_9=\frac{9\times10}{2}=45\). Remember that adding up to (9) uses the factor (10).
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Which is the general formula for \(1+2+3+\cdots+n\)?
D. (\frac{n(n+1)}{2})
पहली (n) प्राकृतिक संख्याओं का योग (S_n=\frac{n(n+1)}{2}) होता है। यह सूत्र इस अध्याय का मूल सूत्र है। / The sum of the first (n) natural numbers is (S_n=\frac{n(n+1)}{2}). This formula is the key formula of this topic.
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If \(S_8\) is the sum of the first (8) natural numbers, what is \(S_8\)?
A. (36)
\(S_8=\frac{8\times9}{2}=36\) है। \(S_n\) में नीचे की संख्या पदों की संख्या बताती है। / \(S_8=\frac{8\times9}{2}=36\). The subscript in \(S_n\) shows the number of terms.
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B. (66)
कुल बिंदु \(1+2+\cdots+11=66\) होंगे। ऐसी व्यवस्था में प्राकृतिक संख्याओं का योग बनता है। / The total dots are \(1+2+\cdots+11=66\). Such an arrangement forms the sum of natural numbers.
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C. (136)
कुल पेज \(S_{16}=\frac{16\times17}{2}=136\) होंगे। प्रश्न में क्रमशः बढ़ते पेज देखें। / Total pages will be \(S_{16}=\frac{16\times17}{2}=136\). Notice the pages increasing one by one in the question.
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What is the sum of the first (4) natural numbers?
D. (10)
(1+2+3+4=10) है। प्राकृतिक संख्याओं की गिनती (0) से नहीं होती। / (1+2+3+4=10). Natural numbers in this topic are not counted from (0).
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If the sum of the first (n) natural numbers is (91), choose (n).
B. (13)
\(S_{13}=\frac{13\times14}{2}=91\) इसलिए (n=13)। सही (n) पहचानने के लिए आसपास के योग जांचें। / \(S_{13}=\frac{13\times14}{2}=91\), so (n=13). Check nearby sums to identify the correct (n).
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What is the sum of natural numbers from (1) to (19)?
C. (190)
\(S_{19}=\frac{19\times20}{2}=190\) होता है। जब अंतिम संख्या (19) हो तो (n=19) लें। / \(S_{19}=\frac{19\times20}{2}=190\). When the last number is (19), take (n=19).
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What will be the sum of the first (2) natural numbers?
B. (3)
पहली (2) प्राकृतिक संख्याएँ (1) और (2) हैं इसलिए योग (3) है। आधारभूत प्रश्नों में सूची बनाना सुरक्षित रहता है। / The first (2) natural numbers are (1) and (2), so the sum is (3). Listing terms is safe in basic questions.
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C. (55)
कुल ईंटें \(1+2+\cdots+10=55\) हैं। सीढ़ी जैसे पैटर्न में अक्सर \(S_n\) लगता है। / Total bricks are \(1+2+\cdots+10=55\). Stair-like patterns often use \(S_n\).
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Find the sum of the first (22) natural numbers.
A. (253)
\(S_{22}=\frac{22\times23}{2}=253\) है। सम संख्या (22) को आधा करके \(11\times23\) करें। / \(S_{22}=\frac{22\times23}{2}=253\). Halve the even number (22) and calculate \(11\times23\).
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If \(1+2+3+\cdots+n=28\), what is the value of (n)?
B. (7)
\(S_7=28\) क्योंकि \(\frac{7\times8}{2}=28\)। योग देखकर निकट प्राकृतिक संख्या चुनें। / \(S_7=28\) because \(\frac{7\times8}{2}=28\). Choose the nearby natural number by observing the sum.
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Which is the sum of the first (17) natural numbers?
C. (153)
\(S_{17}=\frac{17\times18}{2}=153\) है। विषम (n) में अगले सम गुणक को (2) से काटें। / \(S_{17}=\frac{17\times18}{2}=153\). For odd (n), divide the next even factor by (2).
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What will be the sum of \(1+2+3+\cdots+50\)?
D. (1275)
\(S_{50}=\frac{50\times51}{2}=1275\) होता है। बड़े (n) में सूत्र सीधे लगाएं। / \(S_{50}=\frac{50\times51}{2}=1275\). For larger (n), apply the formula directly.
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Which value is equal to the sum of the first (24) natural numbers?
C. (300)
\(S_{24}=\frac{24\times25}{2}=300\) है। (24) का आधा (12) लेकर \(12\times25\) करें। / \(S_{24}=\frac{24\times25}{2}=300\). Take half of (24) as (12) and calculate \(12\times25\).
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If \(S_n=120\) and \(S_n\) is the sum of the first (n) natural numbers, what is (n)?
C. (15)
\(S_{15}=120\) क्योंकि \(\frac{15\times16}{2}=120\)। ऐसे प्रश्नों में उत्तर को वापस सूत्र में जांचें। / \(S_{15}=120\) because \(\frac{15\times16}{2}=120\). In such questions, verify the answer back in the formula.
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What is the sum of the first (40) natural numbers?
C. (820)
\(S_{40}=\frac{40\times41}{2}=820\) है। (40) को (2) से भाग देकर \(20\times41\) करें। / \(S_{40}=\frac{40\times41}{2}=820\). Divide (40) by (2) and calculate \(20\times41\).
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C. (91)
कुल अंक \(1+2+\cdots+13=91\) हैं। अंतिम क्रम संख्या ही (n) का मान देती है। / The total score is \(1+2+\cdots+13=91\). The last rank gives the value of (n).
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Choose the value of the sum of the first (21) natural numbers.
B. (231)
\(S_{21}=\frac{21\times22}{2}=231\) है। अगले सम गुणक (22) को पहले (2) से भाग दें। / \(S_{21}=\frac{21\times22}{2}=231\). Divide the next even factor (22) by (2) first.
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What is the sum of natural numbers from (1) to (35)?
C. (630)
\(S_{35}=\frac{35\times36}{2}=630\) है। अंतिम संख्या (35) को (n) मानें। / \(S_{35}=\frac{35\times36}{2}=630\). Take the last number (35) as (n).
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If \(1+2+3+\cdots+n=210\), what is (n)?
C. (20)
\(S_{20}=\frac{20\times21}{2}=210\) इसलिए (n=20)। बड़े योग में विकल्प से जांच करना सरल है। / \(S_{20}=\frac{20\times21}{2}=210\), so (n=20). For a larger sum, checking through options is simple.
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A chart has numbers from (1) to (23). What is the sum of all the numbers?
C. (276)
सभी नंबरों का योग \(S_{23}=\frac{23\times24}{2}=276\) है। लगातार (1) से शुरू होने पर \(S_n\) लगाएं। / The sum of all numbers is \(S_{23}=\frac{23\times24}{2}=276\). When numbers start consecutively from (1), use \(S_n\).
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Which is the sum of the first (28) natural numbers?
B. (406)
\(S_{28}=\frac{28\times29}{2}=406\) होता है। (28) का आधा (14) लेकर \(14\times29\) करें। / \(S_{28}=\frac{28\times29}{2}=406\). Take half of (28) as (14) and calculate \(14\times29\).
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If \(S_{29}\) is the sum of the first (29) natural numbers, what is the value of \(S_{29}\)?
C. (435)
\(S_{29}=\frac{29\times30}{2}=435\) है। विषम (n) में अगले पद को आधा करके गुणा करें। / \(S_{29}=\frac{29\times30}{2}=435\). For odd (n), halve the next term and multiply.
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Choose the correct sum of \(1+2+3+\cdots+34\).
D. (595)
\(S_{34}=\frac{34\times35}{2}=595\) है। अंतिम पद (34) देखकर सीधे सूत्र लगाएं। / \(S_{34}=\frac{34\times35}{2}=595\). See the last term (34) and apply the formula directly.
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What is the sum of the first (36) natural numbers?
A. (666)
\(S_{36}=\frac{36\times37}{2}=666\) है। (36) को (18) बनाकर \(18\times37\) करें। / \(S_{36}=\frac{36\times37}{2}=666\). Change (36) to (18) and calculate \(18\times37\).
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A teacher asks for the sum of roll numbers from (1) to (31). What is the correct answer?
B. (496)
\(S_{31}=\frac{31\times32}{2}=496\) है। क्रम (1) से शुरू हो तो अंतिम संख्या (n) होती है। / \(S_{31}=\frac{31\times32}{2}=496\). If the sequence starts from (1), the last number is (n).
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Find the sum of the first (45) natural numbers.
C. (1035)
\(S_{45}=\frac{45\times46}{2}=1035\) है। (46) को (23) बनाकर \(45\times23\) करें। / \(S_{45}=\frac{45\times46}{2}=1035\). Change (46) to (23) and calculate \(45\times23\).
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If the sum of the first (n) natural numbers is (325), what will (n) be?
C. (25)
\(S_{25}=\frac{25\times26}{2}=325\) इसलिए (n=25)। दिए गए योग को सूत्र से मिलाकर देखें। / \(S_{25}=\frac{25\times26}{2}=325\), so (n=25). Match the given sum with the formula.
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What is the value of \(1+2+3+\cdots+27\)?
C. (378)
\(S_{27}=\frac{27\times28}{2}=378\) है। (28) को पहले (14) में बदलें। / \(S_{27}=\frac{27\times28}{2}=378\). Change (28) to (14) first.
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Choose the correct option for the sum of the first (33) natural numbers.
B. (561)
\(S_{33}=\frac{33\times34}{2}=561\) है। (34) का आधा (17) लेकर गुणा करें। / \(S_{33}=\frac{33\times34}{2}=561\). Take half of (34) as (17) and multiply.
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C. (171)
कुल सितारे \(S_{18}=\frac{18\times19}{2}=171\) हैं। पंक्ति संख्या बढ़ने पर प्राकृतिक संख्याओं का योग बनता है। / Total stars are \(S_{18}=\frac{18\times19}{2}=171\). Increasing row counts form the sum of natural numbers.
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If \(S_n=465\), what is the value of (n) for the first (n) natural numbers?
C. (30)
\(S_{30}=\frac{30\times31}{2}=465\) इसलिए (n=30)। विकल्पों को सूत्र में रखकर जल्दी उत्तर मिल सकता है। / \(S_{30}=\frac{30\times31}{2}=465\), so (n=30). Substituting options in the formula can give a quick answer.
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What is the sum of the first (100) natural numbers?
B. (5050)
\(S_{100}=\frac{100\times101}{2}=5050\) है। (100) तक के योग का मान याद रखना भी उपयोगी है। / \(S_{100}=\frac{100\times101}{2}=5050\). Remembering the sum up to (100) is also useful.
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What is the sum of the first (37) natural numbers?
B. (703)
\(S_{37}=\frac{37\times38}{2}=703\) है। विषम (n) में अगले सम गुणक को आधा करें। / \(S_{37}=\frac{37\times38}{2}=703\). For odd (n), halve the next even factor.
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Choose the correct sum of \(1+2+3+\cdots+42\).
A. (903)
\(S_{42}=\frac{42\times43}{2}=903\) होता है। सम (n) को (2) से भाग देकर गणना आसान करें। / \(S_{42}=\frac{42\times43}{2}=903\). Divide the even (n) by (2) to make calculation easier.
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If the sum of the first (n) natural numbers is (861), what is the value of (n)?
C. (41)
\(S_{41}=\frac{41\times42}{2}=861\) इसलिए (n=41)। ऐसे प्रश्नों में विकल्पों को सूत्र में रखकर जांचें। / \(S_{41}=\frac{41\times42}{2}=861\), so (n=41). In such questions, check the options in the formula.
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In a school, badge numbers from (1) to (38) are given. What will be the sum of all badge numbers?
B. (741)
सभी बैज नंबरों का योग \(S_{38}=\frac{38\times39}{2}=741\) है। लगातार (1) से शुरू होने पर अंतिम संख्या को (n) मानें। / The sum of all badge numbers is \(S_{38}=\frac{38\times39}{2}=741\). When counting starts from (1), take the last number as (n).
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What is the sum of the first (29) natural numbers?
B. (435)
\(S_{29}=\frac{29\cdot30}{2}=435\)। पहले (30) को (2) से भाग दें। / \(S_{29}=\frac{29\cdot30}{2}=435\). Divide (30) by (2) first.
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Find the sum of the first (31) natural numbers.
B. (496)
\(S_{31}=\frac{31\cdot32}{2}=496\)। सम संख्या को आधा करके गुणा करें। / \(S_{31}=\frac{31\cdot32}{2}=496\). Halve the even number and multiply.
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What will be the value of \(1+2+3+\cdots+33\)?
C. (561)
\(S_{33}=\frac{33\cdot34}{2}=561\)। लंबे जोड़ में सूत्र सबसे तेज तरीका है। / \(S_{33}=\frac{33\cdot34}{2}=561\). The formula is the quickest method for long addition.
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Which is the sum of the first (34) natural numbers?
C. (595)
\(S_{34}=\frac{34\cdot35}{2}=595\)। (34) का आधा (17) लेकर \(17\cdot35\) करें। / \(S_{34}=\frac{34\cdot35}{2}=595\). Take half of (34) as (17) and calculate \(17\cdot35\).
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How much is the sum of the first (37) natural numbers?
B. (703)
\(S_{37}=\frac{37\cdot38}{2}=703\)। (38) का आधा (19) करके गुणा करें। / \(S_{37}=\frac{37\cdot38}{2}=703\). Halve (38) to (19) and multiply.
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What is the sum of \(1+2+3+\cdots+38\)?
A. (741)
\(S_{38}=\frac{38\cdot39}{2}=741\)। पहले (38) को (2) से भाग दें। / \(S_{38}=\frac{38\cdot39}{2}=741\). Divide (38) by (2) first.
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Find the sum of the first (39) natural numbers.
C. (780)
\(S_{39}=\frac{39\cdot40}{2}=780\)। (40) का आधा (20) लेकर \(39\cdot20\) करें। / \(S_{39}=\frac{39\cdot40}{2}=780\). Take half of (40) as (20) and calculate \(39\cdot20\).
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What will be the sum of the first (41) natural numbers?
C. (861)
\(S_{41}=\frac{41\cdot42}{2}=861\)। (42) को (2) से भाग देकर \(21\cdot41\) करें। / \(S_{41}=\frac{41\cdot42}{2}=861\). Divide (42) by (2) and calculate \(21\cdot41\).
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How much is the sum of the first (42) natural numbers?
C. (903)
\(S_{42}=\frac{42\cdot43}{2}=903\)। (42) का आधा (21) करके गुणा करें। / \(S_{42}=\frac{42\cdot43}{2}=903\). Halve (42) to (21) and multiply.
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What is the value of \(1+2+3+\cdots+43\)?
C. (946)
\(S_{43}=\frac{43\cdot44}{2}=946\)। (44) का आधा (22) लेकर \(43\cdot22\) करें। / \(S_{43}=\frac{43\cdot44}{2}=946\). Take half of (44) as (22) and calculate \(43\cdot22\).
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Which is the sum of the first (44) natural numbers?
C. (990)
\(S_{44}=\frac{44\cdot45}{2}=990\)। (44) को आधा करके \(22\cdot45\) करें। / \(S_{44}=\frac{44\cdot45}{2}=990\). Halve (44) and calculate \(22\cdot45\).
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What is the sum of the first (46) natural numbers?
C. (1081)
\(S_{46}=\frac{46\cdot47}{2}=1081\)। (46) का आधा (23) लेकर गुणा करें। / \(S_{46}=\frac{46\cdot47}{2}=1081\). Take half of (46) as (23) and multiply.
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Find the sum of the first (47) natural numbers.
B. (1128)
\(S_{47}=\frac{47\cdot48}{2}=1128\)। (48) का आधा (24) लेकर \(47\cdot24\) करें। / \(S_{47}=\frac{47\cdot48}{2}=1128\). Take half of (48) as (24) and calculate \(47\cdot24\).
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What will be the sum of \(1+2+3+\cdots+48\)?
B. (1176)
\(S_{48}=\frac{48\cdot49}{2}=1176\)। (48) को (2) से भाग देकर \(24\cdot49\) करें। / \(S_{48}=\frac{48\cdot49}{2}=1176\). Divide (48) by (2) and calculate \(24\cdot49\).
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How much is the sum of the first (49) natural numbers?
C. (1225)
\(S_{49}=\frac{49\cdot50}{2}=1225\)। (50) का आधा (25) लेकर \(49\cdot25\) करें। / \(S_{49}=\frac{49\cdot50}{2}=1225\). Take half of (50) as (25) and calculate \(49\cdot25\).
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Which is the sum of the first (52) natural numbers?
C. (1378)
\(S_{52}=\frac{52\cdot53}{2}=1378\)। (52) का आधा (26) लेकर \(26\cdot53\) करें। / \(S_{52}=\frac{52\cdot53}{2}=1378\). Take half of (52) as (26) and calculate \(26\cdot53\).
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If \(S_n=595\), what is the value of (n)?
C. (34)
\(\frac{34\cdot35}{2}=595\), इसलिए (n=34)। विकल्प को सूत्र में रखकर जांचें। / \(\frac{34\cdot35}{2}=595\), so (n=34). Check the option in the formula.
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If the sum of the first (n) natural numbers is (741), what will (n) be?
C. (38)
\(\frac{38\cdot39}{2}=741\), इसलिए (n=38)। ऐसे प्रश्नों में विकल्प जल्दी जांचे जा सकते हैं। / \(\frac{38\cdot39}{2}=741\), so (n=38). In such questions, options can be checked quickly.
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If \(S_n=861\), what is the correct value of (n)?
C. (41)
\(\frac{41\cdot42}{2}=861\), इसलिए (n=41)। उत्तर को सूत्र से अवश्य सत्यापित करें। / \(\frac{41\cdot42}{2}=861\), so (n=41). Always verify the answer with the formula.
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If the sum of the first (n) natural numbers is (990), what is (n)?
C. (44)
\(\frac{44\cdot45}{2}=990\), इसलिए (n=44)। विकल्पों को सूत्र में रखकर मिलान करें। / \(\frac{44\cdot45}{2}=990\), so (n=44). Match the options using the formula.
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If \(S_n=1128\), what will (n) be?
C. (47)
\(\frac{47\cdot48}{2}=1128\), इसलिए (n=47)। (n) खोजने के लिए विकल्पों की जांच आसान है। / \(\frac{47\cdot48}{2}=1128\), so (n=47). Checking options is easy for finding (n).
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If \(S_n=1225\), what will be the value of (n)?
C. (49)
\(\frac{49\cdot50}{2}=1225\), इसलिए (n=49)। सूत्र में विकल्प रखने से उत्तर जल्दी मिलता है। / \(\frac{49\cdot50}{2}=1225\), so (n=49). Substituting options in the formula gives the answer quickly.
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A student added natural numbers from (1) to (29). What sum will be obtained?
C. (435)
(1) से (29) तक का योग \(S_{29}=435\) है। अंतिम संख्या ही (n) होती है। / The sum from (1) to (29) is \(S_{29}=435\). The last number is (n).
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In class, numbers from (1) to (31) were written and their sum was asked. What is the correct answer?
B. (496)
\(S_{31}=\frac{31\cdot32}{2}=496\)। अंतिम संख्या (31) को (n) मानें। / \(S_{31}=\frac{31\cdot32}{2}=496\). Take the last number (31) as (n).
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A list has numbers from (1) to (33). What is their sum?
C. (561)
सूत्र से \(S_{33}=\frac{33\cdot34}{2}=561\)। सूची (1) से शुरू हो तो सीधे प्राकृतिक संख्या का योग लगाएं। / By the formula, \(S_{33}=\frac{33\cdot34}{2}=561\). If the list starts from (1), use the natural-number sum directly.
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A student added all numbers from (1) to (37). What will be the result?
C. (703)
(1) से (37) तक का योग \(\frac{37\cdot38}{2}=703\) है। (38) को आधा करना आसान है। / The sum from (1) to (37) is \(\frac{37\cdot38}{2}=703\). Halving (38) is easy.
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What is the sum of natural numbers from (1) to (42)?
C. (903)
\(S_{42}=\frac{42\cdot43}{2}=903\)। (42) को आधा करके \(21\cdot43\) करें। / \(S_{42}=\frac{42\cdot43}{2}=903\). Halve (42) and calculate \(21\cdot43\).
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In an exercise, \(1+2+3+\cdots+46\) is to be found. What is the correct value?
C. (1081)
\(S_{46}=\frac{46\cdot47}{2}=1081\)। जोड़ लंबा हो तो सूत्र उपयोग करें। / \(S_{46}=\frac{46\cdot47}{2}=1081\). If the addition is long, use the formula.
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Find the sum of the first (54) natural numbers.
C. (1485)
\(S_{54}=\frac{54\cdot55}{2}=1485\)। (54) का आधा (27) लेकर \(27\cdot55\) करें। / \(S_{54}=\frac{54\cdot55}{2}=1485\). Take half of (54) as (27) and calculate \(27\cdot55\).
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How much is the sum of the first (58) natural numbers?
C. (1711)
\(S_{58}=\frac{58\cdot59}{2}=1711\)। (58) को (2) से भाग देकर \(29\cdot59\) करें। / \(S_{58}=\frac{58\cdot59}{2}=1711\). Divide (58) by (2) and calculate \(29\cdot59\).
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What will be the sum of the first (65) natural numbers?
C. (2145)
\(S_{65}=\frac{65\cdot66}{2}=2145\)। (66) का आधा (33) लेकर \(65\cdot33\) करें। / \(S_{65}=\frac{65\cdot66}{2}=2145\). Take half of (66) as (33) and calculate \(65\cdot33\).
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Which is the sum of the first (70) natural numbers?
C. (2485)
\(S_{70}=\frac{70\cdot71}{2}=2485\)। (70) का आधा (35) लेकर गुणा करें। / \(S_{70}=\frac{70\cdot71}{2}=2485\). Take half of (70) as (35) and multiply.
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What is the value of \(1+2+3+\cdots+80\)?
C. (3240)
\(S_{80}=\frac{80\cdot81}{2}=3240\)। (80) का आधा (40) लेकर \(40\cdot81\) करें। / \(S_{80}=\frac{80\cdot81}{2}=3240\). Take half of (80) as (40) and calculate \(40\cdot81\).
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How much is the sum of the first (90) natural numbers?
C. (4095)
\(S_{90}=\frac{90\cdot91}{2}=4095\)। (90) को आधा करके \(45\cdot91\) करें। / \(S_{90}=\frac{90\cdot91}{2}=4095\). Halve (90) and calculate \(45\cdot91\).
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If \(S_n=1485\), what is the value of (n)?
C. (54)
\(\frac{54\cdot55}{2}=1485\), इसलिए (n=54)। विकल्पों को सूत्र में रखकर मिलाएं। / \(\frac{54\cdot55}{2}=1485\), so (n=54). Match the options by putting them in the formula.
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If the sum of the first (n) natural numbers is (2145), what is (n)?
C. (65)
\(\frac{65\cdot66}{2}=2145\), इसलिए (n=65)। सही विकल्प को सूत्र से सत्यापित करें। / \(\frac{65\cdot66}{2}=2145\), so (n=65). Verify the correct option using the formula.
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If \(S_n=3240\), how much is (n)?
C. (80)
\(\frac{80\cdot81}{2}=3240\), इसलिए (n=80)। ऐसे प्रश्नों में विकल्प जांचना सरल रहता है। / \(\frac{80\cdot81}{2}=3240\), so (n=80). In such questions, checking options is simple.
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If \(S_n=4095\), what is the correct value of (n)?
C. (90)
\(\frac{90\cdot91}{2}=4095\), इसलिए (n=90)। उत्तर को सूत्र से एक बार जरूर जांचें। / \(\frac{90\cdot91}{2}=4095\), so (n=90). Check the answer once with the formula.
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A child found the sum of natural numbers from (1) to (54). What is the correct sum?
C. (1485)
(1) से (54) तक का योग \(S_{54}=1485\) है। अंतिम संख्या को (n) मानकर सूत्र लगाएं। / The sum from (1) to (54) is \(S_{54}=1485\). Take the last number as (n) and apply the formula.
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A table contains numbers from (1) to (58). What is their sum?
C. (1711)
\(S_{58}=\frac{58\cdot59}{2}=1711\)। (1) से शुरू होने वाली सूची में प्राकृतिक संख्या योग सूत्र लगाएं। / \(S_{58}=\frac{58\cdot59}{2}=1711\). For a list starting from (1), use the natural-number sum formula.
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What will be the total sum of numbers from (1) to (65)?
C. (2145)
\(S_{65}=\frac{65\cdot66}{2}=2145\)। (66) का आधा (33) लेकर गुणा करें। / \(S_{65}=\frac{65\cdot66}{2}=2145\). Take half of (66) as (33) and multiply.
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A workbook asks \(1+2+3+\cdots+70\). What is the answer?
C. (2485)
\(S_{70}=\frac{70\cdot71}{2}=2485\)। सूत्र से बड़ा जोड़ जल्दी हल होता है। / \(S_{70}=\frac{70\cdot71}{2}=2485\). The formula solves large sums quickly.
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In a question, natural numbers from (1) to (80) are to be added. What is the correct sum?
C. (3240)
(1) से (80) तक का योग \(S_{80}=3240\) है। अंतिम संख्या (80) को (n) मानें। / The sum from (1) to (80) is \(S_{80}=3240\). Take the last number (80) as (n).
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Find the sum of the first (72) natural numbers.
C. (2628)
\(S_{72}=\frac{72\cdot73}{2}=2628\)। (72) का आधा (36) लेकर \(36\cdot73\) करें। / \(S_{72}=\frac{72\cdot73}{2}=2628\). Take half of (72) as (36) and calculate \(36\cdot73\).
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How much is the sum of the first (85) natural numbers?
C. (3655)
\(S_{85}=\frac{85\cdot86}{2}=3655\)। (86) का आधा (43) लेकर \(85\cdot43\) करें। / \(S_{85}=\frac{85\cdot86}{2}=3655\). Take half of (86) as (43) and calculate \(85\cdot43\).
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If \(S_n=2628\), what is the value of (n)?
C. (72)
\(\frac{72\cdot73}{2}=2628\), इसलिए (n=72)। विकल्पों को सूत्र में रखकर मिलान करें। / \(\frac{72\cdot73}{2}=2628\), so (n=72). Match the options by putting them in the formula.
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If \(S_n=3655\), what will (n) be?
C. (85)
\(\frac{85\cdot86}{2}=3655\), इसलिए (n=85)। सही (n) पाने के लिए सूत्र का उपयोग करें। / \(\frac{85\cdot86}{2}=3655\), so (n=85). Use the formula to get the correct (n).
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What will be the sum of the first (95) natural numbers?
C. (4560)
\(S_{95}=\frac{95\cdot96}{2}=4560\)। (96) का आधा (48) लेकर \(95\cdot48\) करें। / \(S_{95}=\frac{95\cdot96}{2}=4560\). Take half of (96) as (48) and calculate \(95\cdot48\).
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If \(S_n=4560\), what is the correct value of (n)?
C. (95)
\(\frac{95\cdot96}{2}=4560\), इसलिए (n=95)। सूत्र में विकल्प रखकर उत्तर जांचें। / \(\frac{95\cdot96}{2}=4560\), so (n=95). Check the answer by substituting options in the formula.
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An exam asked the value of \(1+2+3+\cdots+95\). What is the correct answer?
C. (4560)
\(S_{95}=\frac{95\cdot96}{2}=4560\)। परीक्षा में बड़े योग के लिए सूत्र तुरंत लगाएं। / \(S_{95}=\frac{95\cdot96}{2}=4560\). In exams, apply the formula quickly for large sums.
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