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
8051	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
8052	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 210 ~~ \text{and} ~~ d = 15 $.	1
8053	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 210 ~~ \text{and} ~~ d = 10 $.	1
8054	Find common difference $ d $ of arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ a_{ 30 } = 183 $.	1
8055	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = 0 $.	1
8056	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 8 $.	1
8057	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 53 ~~ \text{and} ~~ d = 7 $.	1
8058	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 16 $.	1
8059	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 8 $.	1
8060	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 8 $.	1
8061	Find $ a_{ 78 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	1
8062	Find $ S_{ 78 } $ ( sum of first $ 78 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	1
8063	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 45 ~~ \text{and} ~~ d = 5 $.	1
8064	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ d = \frac{ 1 }{ 10 } $.	1
8065	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = 6 $.	1
8066	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
8067	Find $ S_{ 1 } $ ( sum of first $ 1 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
8068	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
8069	Find $ a_{ 47 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = \left( -9 \right) $.	1
8070	Find $ S_{ 44 } $ ( sum of first $ 44 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	1
8071	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -35 ~~ \text{and} ~~ d = 2 $.	1
8072	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -35 ~~ \text{and} ~~ d = 23 $.	1
8073	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -99 \right) $.	1
8074	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	1
8075	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	1
8076	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 8 $.	1
8077	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 0 $.	1
8078	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	1
8079	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = \frac{ 24 }{ 5 } $.	1
8080	Find common difference $ d $ of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ a_{ 25 } = 220 $.	1
8081	$$ a_1 = 100 ~,~ d = 5 ~,~ a_n = 25 ~,~ n = ? $$	1
8082	Find $ a_{ 68 } $ of an arithmetic progression if $ a_1 = -19 ~~ \text{and} ~~ d = 14 $.	1
8083	Find $ a_{ 96 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -13 \right) $.	1
8084	$$ a_{ 8 } = 5 ~~,~~ S_{ 15 } = 2 ~~,~~ a_1 = ? ~~,~~ d = ? $$	1
8085	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = 3 $.	1
8086	Find $ a_{ 83 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 3 $.	1
8087	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 10 $.	1
8088	Find $ a_{ 97 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 5 $.	1
8089	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	1
8090	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
8091	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -2 $.	1
8092	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -2 $.	1
8093	Find $ a_{ 199 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 6 } $.	1
8094	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = 1 $.	1
8095	Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = 1 $.	1
8096	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 77 }{ 2 } $.	1
8097	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 18800 ~~ \text{and} ~~ d = 200 $.	1
8098	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 19000 ~~ \text{and} ~~ d = 200 $.	1
8099	Find $ S_{ 49 } $ ( sum of first $ 49 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	1
8100	Find $ a_{ 98 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	1