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
7501	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	1
7502	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 7 $.	1
7503	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 9 $.	1
7504	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = -9 $.	1
7505	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 3 $.	1
7506	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 64 ~~ \text{and} ~~ d = 4 $.	1
7507	Find $ a_{ 64 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	1
7508	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = -32 ~~ \text{and} ~~ d = 6 $.	1
7509	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = -3 $.	1
7510	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = -16 ~~ \text{and} ~~ d = -8 $.	1
7511	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 240 ~~ \text{and} ~~ d = 8 $.	1
7512	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -38 ~~ \text{and} ~~ d = \left( -100 \right) $.	1
7513	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = -7 $.	1
7514	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = -8 $.	1
7515	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 4 $.	1
7516	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 4 $.	1
7517	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $.	1
7518	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 7 $.	1
7519	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -24 ~~ \text{and} ~~ d = \left( -17 \right) $.	1
7520	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 9 $.	1
7521	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 5 $.	1
7522	Find $ S_{ 80 } $ ( sum of first $ 80 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 5 $.	1
7523	Find $ S_{ 71 } $ ( sum of first $ 71 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	1
7524	Find $ a_{ 354 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	1
7525	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 3 } \right) $.	1
7526	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 8 $.	1
7527	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 8 $.	1
7528	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = -4 $.	1
7529	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -13 \right) $.	1
7530	Find $ a_{ 87 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	1
7531	Find $ S_{ 87 } $ ( sum of first $ 87 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	1
7532	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 7 $.	1
7533	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 7 $.	1
7534	Find $ a_{ 51 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 7 $.	1
7535	Find common difference $ d $ of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ a_{ 3 } = 2 $.	1
7536	Find common difference $ d $ of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ a_{ 4 } = 6 $.	1
7537	Find common difference $ d $ of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ a_{ 5 } = 6 $.	1
7538	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 544 ~~ \text{and} ~~ d = 0 $.	1
7539	Find common difference $ d $ of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ a_{ 5 } = 10 $.	1
7540	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 1 $.	1
7541	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
7542	$$ a_1 = \frac{ 21 }{ 10 } ~,~ d = \frac{ 3 }{ 10 } ~,~ a_n = 4 ~,~ n = ? $$	1
7543	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	1
7544	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	1
7545	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 4 }{ 5 } $.	1
7546	$$ a_1 = 4 ~,~ d = \frac{ 5 }{ 2 } ~,~ a_n = 13 ~,~ n = ? $$	1
7547	$$ d = \frac{ 5 }{ 2 } ~,~ a_n = 13 ~,~ S_n = 4 ~,~ n = ? $$	1
7548	Find $ S_{ 84 } $ ( sum of first $ 84 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $.	1
7549	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = -3 $.	1
7550	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 4 $.	1