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 \(S_n=6903\), what is the value of \(S_{n+5}-S_n\)?
B. (600)
\(6903=S_{117}\), इसलिए अंतर (118+119+120+121+122=600) है। अगले पांच पदों का योग लें। / \(6903=S_{117}\), so the difference is (118+119+120+121+122=600). Take the sum of the next five terms.
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What is half of the sum of the first (144) natural numbers?
B. (5220)
\(S_{144}=\frac{144\cdot145}{2}=10440\), इसलिए आधा (5220) है। पहले पूर्ण योग निकालें। / \(S_{144}=\frac{144\cdot145}{2}=10440\), so half is (5220). Find the full sum first.
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If \(S_n-S_{n-3}=420\), what is (n)?
C. (141)
\(S_n-S_{n-3}=3n-3\)। (3n-3=420) से (n=141)। / \(S_n-S_{n-3}=3n-3\). From (3n-3=420), (n=141).
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What is the sum of natural numbers from (63) to (150)?
A. (9369)
योग \(S_{150}-S_{62}=11325-1953=9372\) है। दिए विकल्पों में सही मान नहीं है। / The sum is \(S_{150}-S_{62}=11325-1953=9372\). The listed options do not contain the correct value.
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If \(1+2+3+\cdots+n=8256\), what is the value of (n)?
B. (128)
\(\frac{128\cdot129}{2}=8256\), इसलिए (n=128)। उत्तर को सूत्र से जांचना जरूरी है। / \(\frac{128\cdot129}{2}=8256\), so (n=128). It is important to check the answer with the formula.
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If \(S_n=11325\), what will be \(S_n-S_{n-6}\)?
A. (885)
\(11325=S_{150}\), इसलिए अंतर (145+146+147+148+149+150=885) है। अंतिम छह पदों को जोड़ें। / \(11325=S_{150}\), so the difference is (145+146+147+148+149+150=885). Add the last six terms.
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What is the ratio of the sums of the first (120) and first (80) natural numbers?
B. (121:81)
\(S_{120}:S_{80}=7260:3240=121:54\), इसलिए दिए विकल्पों में सही सरल अनुपात नहीं है। अनुपात को पूरा सरल करें। / \(S_{120}:S_{80}=7260:3240=121:54\), so the listed options do not contain the correct simplified ratio. Simplify fully.
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C. (7525)
परिणाम \(S_{175}-S_{125}=15400-7875=7525\) है। यह (126) से (175) तक का योग है। / The result is \(S_{175}-S_{125}=15400-7875=7525\). This is the sum from (126) to (175).
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If \(S_{n+4}-S_n=490\), what is the value of (n)?
A. (120)
(S_{n+4}-S_n=(n+1)+(n+2)+(n+3)+(n+4)=4n+10)। (4n+10=490) से (n=120)। / (S_{n+4}-S_n=(n+1)+(n+2)+(n+3)+(n+4)=4n+10). From (4n+10=490), (n=120).
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If \(S_n=1225\), what will be the value of \(S_{2n}\)?
C. (4950)
\(1225=S_{49}\), इसलिए (2n=98) और \(S_{98}=\frac{98\cdot99}{2}=4851\)। सही विकल्प (B) होना चाहिए। / \(1225=S_{49}\), so (2n=98) and \(S_{98}=\frac{98\cdot99}{2}=4851\). The correct option should be (B).
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A. (2054)
\(S_{78}-S_{52}+S_{26}=3081-1378+351=2054\)। हर आंशिक योग अलग लिखें। / \(S_{78}-S_{52}+S_{26}=3081-1378+351=2054\). Write each partial sum separately.
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If \(S_n-S_{100}=15150\), what is the value of (n)?
C. (200)
\(S_{200}-S_{100}=20100-5050=15050\), इसलिए दिए विकल्पों में (15150) का सही मिलान नहीं है। अंतर हमेशा जांचें। / \(S_{200}-S_{100}=20100-5050=15050\), so none of the listed options matches (15150). Always check the difference.
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What will be the sum of natural numbers from (81) to (144)?
A. (7200)
योग \(S_{144}-S_{80}=10440-3240=7200\) है। (81) से शुरू हो तो (80) तक का योग घटाएं। / The sum is \(S_{144}-S_{80}=10440-3240=7200\). If it starts from (81), subtract the sum up to (80).
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If \(S_n=7140\), what is the value of \(S_{n+5}-S_n\)?
C. (605)
\(7140=S_{119}\), इसलिए अंतर (120+121+122+123+124=610) है। सही विकल्प (D) होना चाहिए। / \(7140=S_{119}\), so the difference is (120+121+122+123+124=610). The correct option should be (D).
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If \(S_n=8911\), what is the value of (n)?
B. (133)
\(\frac{133\cdot134}{2}=8911\), इसलिए (n=133)। विकल्पों को सूत्र में रखकर सत्यापित करें। / \(\frac{133\cdot134}{2}=8911\), so (n=133). Verify the options by substituting them into the formula.
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What is the difference between the sums of the first (180) and first (90) natural numbers?
A. (12195)
\(S_{180}-S_{90}=16290-4095=12195\)। यह (91) से (180) तक का योग है। / \(S_{180}-S_{90}=16290-4095=12195\). This is the sum from (91) to (180).
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If \(S_{n+1}-S_{n-4}=595\), what will be the value of (n)?
B. (118)
(S_{n+1}-S_{n-4}=(n-3)+(n-2)+(n-1)+n+(n+1)=5n-5)। (5n-5=595) से (n=120)। / (S_{n+1}-S_{n-4}=(n-3)+(n-2)+(n-1)+n+(n+1)=5n-5). From (5n-5=595), (n=120).
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How much is the sum of natural numbers from (201) to (250)?
A. (11275)
योग \(S_{250}-S_{200}=31375-20100=11275\) है। बड़े अंतराल में घटाव विधि तेज होती है। / The sum is \(S_{250}-S_{200}=31375-20100=11275\). The subtraction method is quick for large intervals.
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If \(S_n+S_{n-2}=10000\) and \(S_n-S_{n-2}=199\), what will \(S_n\) be?
B. (5099.5)
दोनों समीकरण जोड़ने पर \(2S_n=10199\), इसलिए \(S_n=5099.5\)। ऐसे मानों से प्रश्न की संगति भी जांचें। / Adding the two equations gives \(2S_n=10199\), so \(S_n=5099.5\). Such values also help check the consistency of the question.
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If \(S_n=15400\), what is the value of \(S_{n-10}\)?
C. (13545)
\(15400=S_{175}\), इसलिए \(S_{165}=\frac{165\cdot166}{2}=13695\) है। दिए विकल्पों में सही मान नहीं है। / \(15400=S_{175}\), so \(S_{165}=\frac{165\cdot166}{2}=13695\). The listed options do not contain the correct value.
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What is the ratio of the sums of the first (96) and first (72) natural numbers?
B. (194:109)
\(S_{96}:S_{72}=4656:2628=194:109\)। अनुपात को सरलतम रूप में लिखें। / \(S_{96}:S_{72}=4656:2628=194:109\). Write the ratio in simplest form.
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If \(S_n-S_{n-3}=348\), what is the value of \(S_n\)?
A. (6670)
\(S_n-S_{n-3}=3n-3\), इसलिए (3n-3=348) से (n=117)। अतः \(S_{117}=6903\) होना चाहिए। / \(S_n-S_{n-3}=3n-3\), so (3n-3=348) gives (n=117). Hence \(S_{117}=6903\).
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What is the sum of natural numbers from (50) to (150)?
A. (10100)
योग \(S_{150}-S_{49}=11325-1225=10100\) है। निचली सीमा से एक कम तक का योग घटाएं। / The sum is \(S_{150}-S_{49}=11325-1225=10100\). Subtract the sum up to one less than the lower limit.
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If \(S_{3n}=1770\), what is the value of (n)?
B. (19)
\(1770=S_{59}\), इसलिए (3n=59) होगा जो पूर्णांक (n) नहीं देता। सही निष्कर्ष है कि कोई पूर्णांक (n) नहीं है। / \(1770=S_{59}\), so (3n=59), which does not give an integer (n). The correct conclusion is no integer (n).
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If \(S_n=20100\), what will be the value of \(S_n-S_{n-8}\)?
A. (1572)
\(20100=S_{200}\), इसलिए अंतर \(193+194+\cdots+200=1572\) है। अंतिम (8) पदों का योग लें। / \(20100=S_{200}\), so the difference is \(193+194+\cdots+200=1572\). Take the sum of the last (8) terms.
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What is the difference between the sum from (1) to (200) and the sum from (1) to (150)?
B. (8775)
\(S_{200}-S_{150}=20100-11325=8775\)। यह (151) से (200) तक का योग है। / \(S_{200}-S_{150}=20100-11325=8775\). This is the sum from (151) to (200).
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If \(S_n-S_{70}=5250\), what is the value of (n)?
B. (125)
\(S_{125}-S_{70}=7875-2485=5390\) नहीं है, इसलिए दिए विकल्पों में (5250) का सही मिलान नहीं है। पहले अंतर की जांच करें। / \(S_{125}-S_{70}=7875-2485=5390\), so none of the listed options matches (5250). Check the difference first.
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If \(S_n=12246\), what is the value of (n)?
C. (156)
\(\frac{156\cdot157}{2}=12246\), इसलिए (n=156)। सम संख्या को आधा करके गुणा करें। / \(\frac{156\cdot157}{2}=12246\), so (n=156). Halve the even number and multiply.
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What is (20%) of the sum of the first (150) natural numbers?
C. (2265)
\(S_{150}=11325\) और \(20%=\frac{1}{5}\), इसलिए मान (2265) है। प्रतिशत को भिन्न में बदलें। / \(S_{150}=11325\) and \(20%=\frac{1}{5}\), so the value is (2265). Convert percentage into a fraction.
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If \(S_{n+2}-S_{n-2}=402\), what will be the value of (n)?
B. (100)
(S_{n+2}-S_{n-2}=(n-1)+n+(n+1)+(n+2)=4n+2)। (4n+2=402) से (n=100)। / (S_{n+2}-S_{n-2}=(n-1)+n+(n+1)+(n+2)=4n+2). From (4n+2=402), (n=100).
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