Arithmetic sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Arithmetic sequences.

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ID	Problem	Count
2251	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	3
2252	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	3
2253	Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 9 $.	3
2254	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = -2 $.	3
2255	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 9 $.	3
2256	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = -\frac{ 49 }{ 10 } ~~ \text{and} ~~ d = \frac{ 4 }{ 5 } $.	3
2257	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	3
2258	Find $ a_1 $ (first term of arithmetic progression) if $ d = 200 ~~ \text{and} ~~ a_{ 12 } = 100 $.	3
2259	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 8 $.	3
2260	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	3
2261	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $.	3
2262	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	3
2263	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	3
2264	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	3
2265	Find $ S_{ 3650 } $ ( sum of first $ 3650 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	3
2266	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	3
2267	Find $ a_{ 81 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 6 $.	3
2268	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	3
2269	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 2250 ~~ \text{and} ~~ d = 150 $.	3
2270	Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	3
2271	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = -\frac{ 1 }{ 2 } $.	3
2272	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = -\frac{ 1 }{ 20 } $.	3
2273	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	3
2274	Find $ S_{ 500 } $ ( sum of first $ 500 $ terms ) of arithmetic progression if $ a_1 = 100000 ~~ \text{and} ~~ d = 100000 $.	3
2275	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = -3 $.	3
2276	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = \left( -5 \right) $.	3
2277	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	3
2278	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -3 \right) $.	3
2279	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 22 $.	3
2280	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 1 $.	3
2281	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	3
2282	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 5 $.	3
2283	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 210 $.	3
2284	Find $ S_{ 120 } $ ( sum of first $ 120 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	3
2285	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	3
2286	$$ a_{ 2 } = -72 ~~,~~ S_{ 6 } = -\frac{ 1 }{ 18 } ~~,~~ a_1 = ? ~~,~~ d = ? $$	3
2287	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 67 ~~ \text{and} ~~ d = -\frac{ 16 }{ 5 } $.	3
2288	Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = -\frac{ 8 }{ 25 } $.	3
2289	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 39 ~~ \text{and} ~~ d = 2 $.	3
2290	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 3 $.	3
2291	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 354 ~~ \text{and} ~~ d = -26 $.	3
2292	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = -6 $.	3
2293	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 5 $.	3
2294	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 500 $.	3
2295	$$ a_1 = 18 ~,~ d = 7 ~,~ a_n = 63 ~,~ n = ? $$	3
2296	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 1 $.	3
2297	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -5 \right) $.	3
2298	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \frac{ 16 }{ 5 } $.	3
2299	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \frac{ 4 }{ 3 } $.	3
2300	$$ a_1 = 6 ~,~ a_n = 25 ~,~ S_n = 625 ~,~ n = ? $$	3