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
7051	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
7052	Find $ S_{ 300 } $ ( sum of first $ 300 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \frac{ 3 }{ 5 } $.	1
7053	Find $ S_{ 64 } $ ( sum of first $ 64 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ d = -\frac{ 1 }{ 3 } $.	1
7054	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = \frac{ 7 }{ 3 } ~~ \text{and} ~~ d = \left( -\frac{ 35 }{ 6 } \right) $.	1
7055	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = \frac{ 7 }{ 3 } ~~ \text{and} ~~ d = -\frac{ 35 }{ 6 } $.	1
7056	Find $ a_{ 76 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	1
7057	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = 120 $.	1
7058	Find $ a_{ 126 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 15 $.	1
7059	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 10 $.	1
7060	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 1500000 ~~ \text{and} ~~ d = 70000 $.	1
7061	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	1
7062	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 81 ~~ \text{and} ~~ d = 5 $.	1
7063	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	1
7064	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	1
7065	Find $ S_{ 46 } $ ( sum of first $ 46 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	1
7066	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	1
7067	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 50 $.	1
7068	$$ a_1 = 69 ~,~ d = 3 ~,~ a_n = 279 ~,~ n = ? $$	1
7069	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 69 ~~ \text{and} ~~ d = 3 $.	1
7070	Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = 64 ~~ \text{and} ~~ d = 2 $.	1
7071	Find $ a_{ 73 } $ of an arithmetic progression if $ a_1 = 64 ~~ \text{and} ~~ d = 2 $.	1
7072	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 1 $.	1
7073	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = \left( -27 \right) $.	1
7074	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -18 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
7075	$$ a_1 = 9 ~,~ d = 3 ~,~ a_n = 90 ~,~ n = ? $$	1
7076	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = \left( -\frac{ 3 }{ 2 } \right) $.	1
7077	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 335000 ~~ \text{and} ~~ d = 6200 $.	1
7078	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 335000 ~~ \text{and} ~~ d = 6200 $.	1
7079	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 4 $.	1
7080	Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 7 $.	1
7081	Find $ S_{ 51 } $ ( sum of first $ 51 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 8 $.	1
7082	Find $ S_{ 68 } $ ( sum of first $ 68 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 14 $.	1
7083	Find $ S_{ 237 } $ ( sum of first $ 237 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 9 $.	1
7084	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	1
7085	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = -\frac{ 5 }{ 4 } ~~ \text{and} ~~ d = 0 $.	1
7086	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = -80 ~~ \text{and} ~~ d = 3 $.	1
7087	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -80 ~~ \text{and} ~~ d = 3 $.	1
7088	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = -4 $.	1
7089	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -80 ~~ \text{and} ~~ d = 3 $.	1
7090	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = -\frac{ 1 }{ 2 } $.	1
7091	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 8 $.	1
7092	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = 0 $.	1
7093	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = -4 $.	1
7094	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 50876 ~~ \text{and} ~~ d = 1500 $.	1
7095	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 11 $.	1
7096	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 8 $.	1
7097	Find $ S_{ 47 } $ ( sum of first $ 47 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
7098	Find $ a_{ 73 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 3 $.	1
7099	Find $ a_{ 51 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 9 $.	1
7100	$$ a_{ 4 } = -11 ~~,~~ S_{ 18 } = -39 ~~,~~ a_1 = ? ~~,~~ d = ? $$	1