sequences se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
3683 questions tagged with sequences.
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 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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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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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 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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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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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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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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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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