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
8151	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 12 $.	1
8152	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	1
8153	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	1
8154	Find $ S_{ 400 } $ ( sum of first $ 400 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	1
8155	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	1
8156	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
8157	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = -2 $.	1
8158	Find $ S_{ 370 } $ ( sum of first $ 370 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	1
8159	Find $ a_{ 175 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	1
8160	Find $ S_{ 175 } $ ( sum of first $ 175 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	1
8161	Find $ S_{ 58 } $ ( sum of first $ 58 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	1
8162	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	1
8163	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 9 $.	1
8164	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	1
8165	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = \frac{ 73 }{ 5 } $.	1
8166	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = \frac{ 73 }{ 5 } $.	1
8167	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = \frac{ 73 }{ 5 } $.	1
8168	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 8 $.	1
8169	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -16 $.	1
8170	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 52 ~~ \text{and} ~~ d = \left( -9 \right) $.	1
8171	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = \left( -12 \right) $.	1
8172	$$ a_1 = 5 ~,~ d = 3 ~,~ a_n = 20 ~,~ n = ? $$	1
8173	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 1 $.	1
8174	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = \frac{ 13 }{ 2 } ~~ \text{and} ~~ d = \left( -2 \right) $.	1
8175	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = \frac{ 149 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
8176	$$ a_1 = 2 ~,~ d = 9 ~,~ S_n = 3350 ~,~ n = ? $$	1
8177	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 8 $.	1
8178	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = 2 $.	1
8179	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
8180	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	1
8181	Find $ a_{ 49 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = 5 $.	1
8182	Find $ a_{ 65 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 8 $.	1
8183	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = \left( -7 \right) $.	1
8184	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 10 $.	1
8185	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	1
8186	Find $ S_{ 500 } $ ( sum of first $ 500 $ terms ) of arithmetic progression if $ a_1 = 126 ~~ \text{and} ~~ d = 126 $.	1
8187	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 3 $.	1
8188	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 12 $.	1
8189	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = \left( -12 \right) $.	1
8190	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -22 ~~ \text{and} ~~ d = \left( -8 \right) $.	1
8191	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -22 ~~ \text{and} ~~ d = 8 $.	1
8192	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 5 $.	1
8193	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $.	1
8194	Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 3 }{ 10 } $.	1
8195	Find $ S_{ 41 } $ ( sum of first $ 41 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 3 }{ 10 } $.	1
8196	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 1700 ~~ \text{and} ~~ d = 11 $.	1
8197	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 1 $.	1
8198	Find $ a_{ 87 } $ of an arithmetic progression if $ a_1 = 105 ~~ \text{and} ~~ d = \left( -10 \right) $.	1
8199	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 5 }{ 6 } $.	1
8200	Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ a_{ 13 } = 15 $.	1