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 (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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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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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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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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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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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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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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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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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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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 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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 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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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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