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
7151	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 91 ~~ \text{and} ~~ d = 1 $.	1
7152	$$ a_1 = 5 ~,~ d = -3 ~,~ S_n = -85 ~,~ n = ? $$	1
7153	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 14 $.	1
7154	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 99 ~~ \text{and} ~~ d = 14 $.	1
7155	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 11 $.	1
7156	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 41 ~~ \text{and} ~~ d = 3 $.	1
7157	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = -3 $.	1
7158	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = -8 $.	1
7159	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	1
7160	$$ a_1 = 3 ~,~ d = 5 ~,~ S_n = 40 ~,~ n = ? $$	1
7161	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 7 $.	1
7162	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 3 $.	1
7163	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 0 $.	1
7164	Find $ a_{ 933 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 12 $.	1
7165	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 7 $.	1
7166	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -85 \right) $.	1
7167	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -55 \right) $.	1
7168	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
7169	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	1
7170	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	1
7171	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 3 $.	1
7172	Find $ a_{ 51 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	1
7173	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 3 $.	1
7174	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 2 $.	1
7175	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	1
7176	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	1
7177	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 12 $.	1
7178	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 25 } ~~ \text{and} ~~ d = 12 $.	1
7179	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 25 } ~~ \text{and} ~~ d = \frac{ 3 }{ 25 } $.	1
7180	Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 25 } ~~ \text{and} ~~ d = \frac{ 3 }{ 25 } $.	1
7181	Find $ S_{ 3650 } $ ( sum of first $ 3650 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
7182	Find $ S_{ 9125 } $ ( sum of first $ 9125 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
7183	Find $ S_{ 37 } $ ( sum of first $ 37 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $.	1
7184	Find $ a_{ 300 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 0 $.	1
7185	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 5 $.	1
7186	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = -3 $.	1
7187	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = -7 $.	1
7188	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 51 ~~ \text{and} ~~ d = -7 $.	1
7189	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 5 $.	1
7190	Find $ S_{ 102 } $ ( sum of first $ 102 $ terms ) of arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 27 $.	1
7191	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 65 ~~ \text{and} ~~ d = -8 $.	1
7192	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	1
7193	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 51 ~~ \text{and} ~~ d = -4 $.	1
7194	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 99 ~~ \text{and} ~~ d = 11 $.	1
7195	Find $ S_{ 27 } $ ( sum of first $ 27 $ terms ) of arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 0 $.	1
7196	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $.	1
7197	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 3 $.	1
7198	$$ a_1 = 11 ~,~ d = 7 ~,~ a_n = 6 ~,~ n = ? $$	1
7199	Find $ S_{ 120 } $ ( sum of first $ 120 $ terms ) of arithmetic progression if $ a_1 = 3200 ~~ \text{and} ~~ d = -25 $.	1
7200	Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ a_{ 12 } = 27 $.	1