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
9051	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 5 $.	1
9052	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -32 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
9053	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 17 $.	1
9054	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 33 ~~ \text{and} ~~ d = 17 $.	1
9055	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 10 $.	1
9056	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 23 }{ 10 } ~~ \text{and} ~~ d = \frac{ 43 }{ 100 } $.	1
9057	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	1
9058	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 8 $.	1
9059	Find $ a_{ 63 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = \left( -7 \right) $.	1
9060	Find $ S_{ 581 } $ ( sum of first $ 581 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 12 $.	1
9061	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 5 $.	1
9062	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 4 $.	1
9063	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = -47 ~~ \text{and} ~~ d = 8 $.	1
9064	Find $ S_{ 60000 } $ ( sum of first $ 60000 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	1
9065	Find $ S_{ 60000 } $ ( sum of first $ 60000 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 0 $.	1
9066	Find $ a_{ 60000 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	1
9067	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 25 $.	1
9068	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 50 $.	1
9069	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 50 $.	1
9070	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 45 $.	1
9071	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 48 $.	1
9072	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 47 $.	1
9073	Find $ S_{ 80 } $ ( sum of first $ 80 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 50 $.	1
9074	Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $.	1
9075	Find $ a_{ 125 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 8 $.	1
9076	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 2 $.	1
9077	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	1
9078	Find $ a_{ 120 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	1
9079	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	1
9080	Find $ S_{ 365 } $ ( sum of first $ 365 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	1
9081	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 11 }{ 2 } $.	1
9082	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	1
9083	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 7 }{ 2 } $.	1
9084	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 2 $.	1
9085	Find $ S_{ 112 } $ ( sum of first $ 112 $ terms ) of arithmetic progression if $ a_1 = 545 ~~ \text{and} ~~ d = 4 $.	1
9086	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 8 $.	1
9087		1
9088	Find $ a_{ 86 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 16 $.	1
9089	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 2 $.	1
9090	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 500 $.	1
9091	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 6 $.	1
9092	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 6 $.	1
9093	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = -5 $.	1
9094	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
9095	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = \left( -7 \right) $.	1
9096	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 11 $.	1
9097	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	1
9098	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 1 $.	1
9099	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 80 ~~ \text{and} ~~ d = -16 $.	1
9100	$$ a_1 = 80 ~,~ d = -16 ~,~ S_n = 144 ~,~ n = ? $$	1