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 \(S_n=7875\), what is the value of \(S_{n-7}\)?
C. (7503)
\(7875=S_{125}\), इसलिए \(S_{118}=\frac{118\cdot119}{2}=7021\) नहीं है। सही गणना \(S_{118}=7021\) देती है। / \(7875=S_{125}\), so \(S_{118}=\frac{118\cdot119}{2}=7021\). The listed options should be checked carefully.
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Find the sum of natural numbers from (126) to (175).
A. (7525)
योग \(S_{175}-S_{125}=15400-7875=7525\) है। \(S_b-S_{a-1}\) विधि उपयोग करें। / The sum is \(S_{175}-S_{125}=15400-7875=7525\). Use the \(S_b-S_{a-1}\) method.
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If \(S_n+S_{n-1}=4212\) and \(S_n-S_{n-1}=65\), what is the value of \(S_n\)?
A. (2138.5)
दोनों समीकरण जोड़ने पर \(2S_n=4277\), इसलिए \(S_n=2138.5\)। दिए गए आंकड़ों की संगति भी जांचें। / Adding the two equations gives \(2S_n=4277\), so \(S_n=2138.5\). Also check the consistency of the given data.
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What is the ratio of the sums of the first (64) and first (32) natural numbers?
A. (65:33)
\(S_{64}:S_{32}=2080:528=65:33\)। अनुपात को सरलतम रूप में लिखें। / \(S_{64}:S_{32}=2080:528=65:33\). Write the ratio in simplest form.
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If \(S_n=5050\), what is the value of \(S_{n+4}-S_n\)?
B. (410)
\(5050=S_{100}\), इसलिए अंतर (101+102+103+104=410) है। अगले पदों को सीधे जोड़ें। / \(5050=S_{100}\), so the difference is (101+102+103+104=410). Add the next terms directly.
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What is the difference between the sums of the first (120) and first (85) natural numbers?
C. (3605)
\(S_{120}-S_{85}=7260-3655=3605\)। यह (86) से (120) तक का योग है। / \(S_{120}-S_{85}=7260-3655=3605\). This is the sum from (86) to (120).
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If \(S_{n+3}-S_n=222\), what is the value of (n)?
B. (72)
(S_{n+3}-S_n=(n+1)+(n+2)+(n+3)=3n+6)। (3n+6=222) से (n=72)। / (S_{n+3}-S_n=(n+1)+(n+2)+(n+3)=3n+6). From (3n+6=222), (n=72).
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If \(S_n-S_{n-5}=490\), what will be the value of (n)?
C. (100)
(S_n-S_{n-5}=(n-4)+(n-3)+(n-2)+(n-1)+n=5n-10)। (5n-10=490) से (n=100)। / (S_n-S_{n-5}=(n-4)+(n-3)+(n-2)+(n-1)+n=5n-10). From (5n-10=490), (n=100).
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What is the sum of natural numbers from (41) to (95)?
A. (3740)
योग \(S_{95}-S_{40}=4560-820=3740\) है। सीमा से पहले तक का योग जरूर घटाएं। / The sum is \(S_{95}-S_{40}=4560-820=3740\). Always subtract the sum before the lower limit.
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If (S_n=\frac{n(n+1)}{2}) and \(S_n=6670\), what is the value of (n)?
C. (115)
\(\frac{115\cdot116}{2}=6670\), इसलिए (n=115)। बड़े मानों में विकल्पों को सूत्र में रखकर जांचें। / \(\frac{115\cdot116}{2}=6670\), so (n=115). For large values, check options in the formula.
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If \(S_y=15931\), what will be the value of \(S_{y+3}\)?
A. (16435)
\(S_{178}=15931\) है इसलिए \(S_{181}=15931+179+180+181=16471\)। तीन आगे जाने पर अगले तीन पद जोड़ें। / \(S_{178}=15931\), so \(S_{181}=15931+179+180+181=16471\). To move three steps ahead, add the next three terms.
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What is (4) times the difference between \(S_{96}\) and \(S_{48}\)?
A. (13920)
\(S_{96}-S_{48}=4656-1176=3480\) और \(4\times3480=13920\) है। पहले अंतर निकालें फिर गुणा करें। / \(S_{96}-S_{48}=4656-1176=3480\), and \(4\times3480=13920\). First find the difference and then multiply.
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If \(S_n=20100\), what is the value of (n)?
C. (200)
\(S_{200}=\frac{200\times201}{2}=20100\) इसलिए (n=200) है। \(2S_n\) को क्रमागत गुणनफल से मिलाएं। / \(S_{200}=\frac{200\times201}{2}=20100\), so (n=200). Match \(2S_n\) with a consecutive product.
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What is the value of \(S_{300}-S_{285}\)?
B. (4395)
अंतर \(286+287+\cdots+300=4395\) है। बड़े सूचकांकों में भी केवल बीच के पद जोड़ने होते हैं। / The difference is \(286+287+\cdots+300=4395\). Even with large indices, only the terms in between need to be added.
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If \(S_{n+3}-S_{n-3}=615\), what will be the value of (n)?
D. (102)
अंतर ((n-2)+(n-1)+n+(n+1)+(n+2)+(n+3)=6n+3) है और (6n+3=615) से (n=102)। बीच के छह पदों का योग बनाएं। / The difference is ((n-2)+(n-1)+n+(n+1)+(n+2)+(n+3)=6n+3), and (6n+3=615) gives (n=102). Form the sum of the six middle terms.
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The sum of the first (n) natural numbers is (13695). What is the value of (n-30)?
B. (135)
\(S_{165}=13695\) इसलिए (n=165) और (n-30=135)। पहले (n) निकालें फिर पूछा गया मान दें। / \(S_{165}=13695\), so (n=165) and (n-30=135). Find (n) first and then answer what is asked.
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Find the value of \(S_{37}+S_{74}+S_{111}\).
A. (9775)
\(S_{37}=703\), \(S_{74}=2775\) और \(S_{111}=6216\), इसलिए कुल (9694) है। तीन अलग सूचकांकों को ध्यान से जोड़ें। / \(S_{37}=703\), \(S_{74}=2775\), and \(S_{111}=6216\), so the total is (9694). Add the three different indices carefully.
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If \(S_n=11781\), what is the value of (n)?
C. (153)
\(S_{153}=\frac{153\times154}{2}=11781\) इसलिए (n=153) है। बड़े मानों में \(2S_n\) से पहचान आसान होती है। / \(S_{153}=\frac{153\times154}{2}=11781\), so (n=153). For large values, using \(2S_n\) makes identification easier.
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Which sum is obtained by adding \(133+134+\cdots+140\) to \(S_{132}\)?
C. \(S_{140}\)
\(S_{132}+133+134+\cdots+140=S_{140}\) है। लगातार नए पद जुड़ने पर अंतिम पद नया सूचकांक बनता है। / \(S_{132}+133+134+\cdots+140=S_{140}\). When consecutive new terms are added, the last term becomes the new index.
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If \(S_n-S_{n-1}=154\) and \(S_m=7503\), what is (n-m)?
B. (31)
पहले (n=154) और \(S_m=7503\) से (m=122), इसलिए (n-m=32)। लगातार योगों का अंतर सूचकांक देता है। / First (n=154), and \(S_m=7503\) gives (m=122), so (n-m=32). The difference of consecutive sums gives the index.
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C. (7525)
अंतर \(S_{175}-S_{125}=15400-7875=7525\) है। यह (126) से (175) तक के पदों का योग है। / The difference is \(S_{175}-S_{125}=15400-7875=7525\). It is the sum from (126) to (175).
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What is the value of \(S_{48}+S_{96}-S_{32}\)?
B. (5294)
(1176+4656-528=5304) है। हर \(S_n\) का मान पहले लिखकर फिर क्रिया करें। / (1176+4656-528=5304). Write the value of each \(S_n\) first and then perform the operation.
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If \(S_x=8385\), what is the value of (x)?
B. (129)
\(S_{129}=\frac{129\times130}{2}=8385\) इसलिए (x=129) है। \(2S_x\) करके क्रमागत गुणनफल खोजें। / \(S_{129}=\frac{129\times130}{2}=8385\), so (x=129). Use \(2S_x\) to find the consecutive product.
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A. (11172)
कुल वाहन \(7S_{56}=7\times1596=11172\) हैं। (7r) जैसे पैटर्न में (7) को योग के बाहर लें। / Total vehicles are \(7S_{56}=7\times1596=11172\). In a pattern like (7r), take (7) outside the sum.
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At which (n) will \(S_n\) first become greater than (30000)?
B. (245)
\(S_{244}=29890\) और \(S_{245}=30135\) है इसलिए पहली बार (n=245) पर योग (30000) से अधिक होगा। आसपास के मान जांचना सबसे सुरक्षित है। / \(S_{244}=29890\) and \(S_{245}=30135\), so it first exceeds (30000) at (n=245). Checking nearby values is the safest method.
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If \(S_n=4656\), what is the value of \(S_{n+12}-S_n\)?
A. (1230)
\(S_{96}=4656\) इसलिए अंतर \(97+98+\cdots+108=1230\) है। आगे के (12) पदों का योग अलग से निकालें। / \(S_{96}=4656\), so the difference is \(97+98+\cdots+108=1230\). Find the sum of the next (12) terms separately.
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What is the sum of \(151+152+153+\cdots+210\)?
A. (10830)
योग \(S_{210}-S_{150}=22155-11325=10830\) है। (151) से शुरू होने पर (150) तक का योग घटाएं। / The sum is \(S_{210}-S_{150}=22155-11325=10830\). When starting from (151), subtract the sum up to (150).
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If \(S_{2k+3}=3240\), what will be the value of (k)?
D. (40)
\(S_{80}=3240\) इसलिए (2k+3=80) से पूर्णांक (k) नहीं मिलता। सूचकांक में दी गई शर्त को भी जांचें। / \(S_{80}=3240\), so (2k+3=80) gives no integer (k). Check the given index condition too.
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Find the value of \(S_{180}-S_{170}+S_{20}\).
B. (1975)
(16290-14535+210=1965) है। पहले घटाव करें फिर छोटे योग को जोड़ें। / (16290-14535+210=1965). First subtract and then add the smaller sum.
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What is the sum of the first (250) natural numbers?
B. (31375)
\(S_{250}=\frac{250\times251}{2}=31375\) है। बड़े (n) में पहले (250) को (125) बनाएं। / \(S_{250}=\frac{250\times251}{2}=31375\). For large (n), first change (250) to (125).
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