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
5051	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
5052	$$ a_1 = 24 ~~,~~ d = 8 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
5053	Find $ a_{ 498 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
5054	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	2
5055	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $.	2
5056	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 20 $.	2
5057	Find $ S_{ 29 } $ ( sum of first $ 29 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
5058	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 47 ~~ \text{and} ~~ d = 0 $.	2
5059	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
5060	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 44 ~~ \text{and} ~~ d = 0 $.	2
5061	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 68 ~~ \text{and} ~~ d = 7 $.	2
5062	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
5063	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 63 ~~ \text{and} ~~ d = 6 $.	2
5064	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 57 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
5065	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 61 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
5066	Find common difference $ d $ of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ a_{ 50 } = 331 $.	2
5067	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -7 $.	2
5068	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
5069	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = \frac{ 19 }{ 2 } ~~ \text{and} ~~ d = \frac{ 8 }{ 5 } $.	2
5070	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 3 $.	2
5071	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 7 $.	2
5072	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 72 ~~ \text{and} ~~ d = 6 $.	2
5073	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 3 $.	2
5074	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
5075	Find $ a_{ 71 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
5076	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5077	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 0 $.	2
5078	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 7 $.	2
5079	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $.	2
5080	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $.	2
5081	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 6 $.	2
5082	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = \frac{ 56 }{ 5 } ~~ \text{and} ~~ d = \frac{ 27 }{ 5 } $.	2
5083	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -16 ~~ \text{and} ~~ d = 6 $.	2
5084	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
5085	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
5086	Find $ S_{ 54 } $ ( sum of first $ 54 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
5087	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 70000 ~~ \text{and} ~~ d = 900 $.	2
5088	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
5089	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = -5 $.	2
5090	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = -5 $.	2
5091	Find $ S_{ 499 } $ ( sum of first $ 499 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
5092	Find $ S_{ 499 } $ ( sum of first $ 499 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = -2 $.	2
5093	Find $ S_{ 499 } $ ( sum of first $ 499 $ terms ) of arithmetic progression if $ a_1 = 998 ~~ \text{and} ~~ d = -2 $.	2
5094	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 6 $.	2
5095	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2
5096	$$ a_1 = 14 ~,~ d = 4 ~,~ S_n = 8174 ~,~ n = ? $$	2
5097	Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5098	Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 2 $.	2
5099	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	2
5100	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = 6 $.	2