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 (2211), what is (n)?
B. (66)
\(\frac{66\cdot67}{2}=2211\), इसलिए (n=66)। गुणा करने से पहले सम संख्या को आधा करें। / \(\frac{66\cdot67}{2}=2211\), so (n=66). Halve the even number before multiplying.
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What is the difference between the sums of the first (90) and first (85) natural numbers?
C. (440)
\(S_{90}-S_{85}=4095-3655=440\)। यह (86) से (90) तक का योग है। / \(S_{90}-S_{85}=4095-3655=440\). This is the sum from (86) to (90).
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If \(S_n=2016\), what is the value of (n)?
C. (63)
\(\frac{63\cdot64}{2}=2016\), इसलिए (n=63)। सूत्र से विकल्पों का मिलान करें। / \(\frac{63\cdot64}{2}=2016\), so (n=63). Match the options using the formula.
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Which sum is obtained by adding (37+38) to the sum of the first (36) natural numbers?
B. \(S_{38}\)
\(S_{36}+37+38=S_{38}\) होता है। लगातार अगले पद जोड़ने से आगे का आंशिक योग मिलता है। / \(S_{36}+37+38=S_{38}\). Adding consecutive next terms gives the later partial sum.
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What is the sum of natural numbers from (56) to (65)?
B. (605)
योग \(S_{65}-S_{55}=2145-1540=605\) है। बीच की संख्याओं के लिए घटाव विधि उपयोगी है। / The sum is \(S_{65}-S_{55}=2145-1540=605\). The subtraction method is useful for middle numbers.
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If \(S_n-S_{n-1}=68\), what will be \(S_n\)?
B. (2346)
\(S_n-S_{n-1}=n\), इसलिए (n=68) और \(S_{68}=\frac{68\cdot69}{2}=2346\)। अंतर से (n) पहचानें। / \(S_n-S_{n-1}=n\), so (n=68) and \(S_{68}=\frac{68\cdot69}{2}=2346\). Identify (n) from the difference.
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If \(S_n=2850\), what will be the value of \(S_{n-5}\)?
A. (2485)
\(2850=S_{75}\), इसलिए \(S_{70}=2485\)। पहले (n) पहचानकर (5) कम करें। / \(2850=S_{75}\), so \(S_{70}=2485\). First identify (n) and then reduce it by (5).
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C. (225)
\(S_{20}+S_5=210+15=225\)। दोनों अलग-अलग योग निकालकर जोड़ें। / \(S_{20}+S_5=210+15=225\). Find both sums separately and add them.
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How much will be the sum of natural numbers from (71) to (80)?
B. (755)
योग \(S_{80}-S_{70}=3240-2485=755\) है। यह (10) लगातार संख्याओं का योग है। / The sum is \(S_{80}-S_{70}=3240-2485=755\). This is the sum of (10) consecutive numbers.
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If the sum of the first (n) natural numbers is (1540), what is (n)?
C. (55)
\(\frac{55\cdot56}{2}=1540\), इसलिए (n=55)। विकल्पों को सूत्र में रखकर मिलाएं। / \(\frac{55\cdot56}{2}=1540\), so (n=55). Match the options by putting them in the formula.
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What is the difference between the sums of the first (28) and first (14) natural numbers?
B. (301)
\(S_{28}-S_{14}=406-105=301\)। अंतर निकालते समय छोटे योग को घटाएं। / \(S_{28}-S_{14}=406-105=301\). Subtract the smaller sum while finding the difference.
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If \(S_n-S_{20}=250\), what is the correct value of (n)?
B. (29)
\(S_{29}-S_{20}=435-210=225\) नहीं होता, इसलिए विकल्पों को दोबारा जांचना चाहिए। सही मान (30) है क्योंकि (465-210=255) भी नहीं है। / The options should be checked carefully because \(S_n-S_{20}=250\) does not match the listed values. No listed option gives exactly (250).
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What is the sum of natural numbers from (46) to (55)?
B. (505)
योग \(S_{55}-S_{45}=1540-1035=505\) है। लगातार (10) पदों का औसत \(\frac{46+55}{2}\) भी ले सकते हैं। / The sum is \(S_{55}-S_{45}=1540-1035=505\). You can also use the average of (10) consecutive terms.
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If \(S_n=231\), what will be \(S_{n+4}\)?
B. (351)
\(231=S_{21}\), इसलिए \(S_{25}=\frac{25\cdot26}{2}=325\)। दिए गए (n) को पहचानकर (4) आगे बढ़ें। / \(231=S_{21}\), so \(S_{25}=\frac{25\cdot26}{2}=325\). Identify the given (n) and move (4) ahead.
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A. (24:11)
\(S_{15}:S_{10}=120:55=24:11\)। अनुपात को सबसे छोटे रूप में लिखें। / \(S_{15}:S_{10}=120:55=24:11\). Write the ratio in its simplest form.
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If \(S_n=1176\), what will be \(S_{n-1}\)?
B. (1128)
\(1176=S_{48}\), इसलिए \(S_{47}=1128\)। पिछले योग के लिए (n)वां पद घटा सकते हैं। / \(1176=S_{48}\), so \(S_{47}=1128\). For the previous sum, you can subtract the (n)th term.
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B. (955)
\(S_{100}-S_{90}=5050-4095=955\)। यह (91) से (100) तक का योग है। / \(S_{100}-S_{90}=5050-4095=955\). This is the sum from (91) to (100).
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If \(1+2+3+\cdots+n=2080\), what will be the value of (n)?
C. (64)
\(\frac{64\cdot65}{2}=2080\), इसलिए (n=64)। बड़े (n) में विकल्पों से मिलान करें। / \(\frac{64\cdot65}{2}=2080\), so (n=64). For large (n), match using the options.
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Find the sum of natural numbers from (36) to (45).
B. (405)
योग \(S_{45}-S_{35}=1035-630=405\) है। (36) से शुरू हो तो (35) तक का योग घटाएं। / The sum is \(S_{45}-S_{35}=1035-630=405\). If it starts from (36), subtract the sum up to (35).
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If \(S_n-S_{n-3}=114\), what is the value of (n)?
C. (40)
(S_n-S_{n-3}=(n-2)+(n-1)+n=3n-3) है। (3n-3=114) से (n=39) नहीं बल्कि विकल्पों में सही मान नहीं है। / (S_n-S_{n-3}=(n-2)+(n-1)+n=3n-3). From (3n-3=114), (n=39), so no listed option is correct.
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If \(S_n=300\), what will be \(S_{n+3}\)?
B. (378)
\(300=S_{24}\), इसलिए \(S_{27}=\frac{27\cdot28}{2}=378\)। पहले (n) पहचानें फिर (3) आगे बढ़ें। / \(300=S_{24}\), so \(S_{27}=\frac{27\cdot28}{2}=378\). Identify (n) first and then move (3) ahead.
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What is the difference between the sums of the first (80) and first (75) natural numbers?
A. (390)
\(S_{80}-S_{75}=3240-2850=390\)। यह (76) से (80) तक का योग है। / \(S_{80}-S_{75}=3240-2850=390\). This is the sum from (76) to (80).
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How much is the sum of natural numbers from (51) to (60)?
C. (555)
योग \(S_{60}-S_{50}=1830-1275=555\) है। यह लगातार (10) संख्याओं का योग है। / The sum is \(S_{60}-S_{50}=1830-1275=555\). This is the sum of (10) consecutive numbers.
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C. (53)
\(\frac{53\cdot54}{2}=1431\), इसलिए (n=53)। उत्तर को सूत्र से सत्यापित करें। / \(\frac{53\cdot54}{2}=1431\), so (n=53). Verify the answer with the formula.
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What is the value of \(1+2+3+\cdots+64\)?
C. (2080)
\(S_{64}=\frac{64\cdot65}{2}=2080\)। बड़े योग के लिए सूत्र का सीधा उपयोग करें। / \(S_{64}=\frac{64\cdot65}{2}=2080\). Use the formula directly for large sums.
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What is half of the sum of the first (24) natural numbers?
B. (150)
\(S_{24}=300\), इसलिए आधा (150) है। पहले पूर्ण योग निकालकर फिर भाग दें। / \(S_{24}=300\), so half is (150). First find the full sum and then divide.
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If \(S_n-S_{n-2}=79\), what is the value of (n)?
C. (40)
(S_n-S_{n-2}=(n-1)+n=2n-1) है। (2n-1=79) से (n=40)। / (S_n-S_{n-2}=(n-1)+n=2n-1). From (2n-1=79), (n=40).
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If \(S_n=990\), what will be \(S_{n-2}\)?
B. (903)
\(990=S_{44}\), इसलिए \(S_{42}=\frac{42\cdot43}{2}=903\)। (n) पहचानकर दो पद पीछे जाएं। / \(990=S_{44}\), so \(S_{42}=\frac{42\cdot43}{2}=903\). Identify (n) and move two terms back.
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What is the difference between the sums of the first (70) and first (60) natural numbers?
C. (655)
\(S_{70}-S_{60}=2485-1830=655\)। यह (61) से (70) तक का योग है। / \(S_{70}-S_{60}=2485-1830=655\). This is the sum from (61) to (70).
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Find the sum of natural numbers from (26) to (35).
B. (305)
योग \(S_{35}-S_{25}=630-325=305\) है। (26) से शुरू हो तो (25) तक का योग घटाएं। / The sum is \(S_{35}-S_{25}=630-325=305\). If it starts from (26), subtract the sum up to (25).
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