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
9151	$$ a_{ 5 } = 13 ~~,~~ S_{ 13 } = 169 ~~,~~ a_1 = ? ~~,~~ d = ? $$	1
9152	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 0 $.	1
9153	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -4 $.	1
9154	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $.	1
9155	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = -3 $.	1
9156	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 150 $.	1
9157	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = \frac{ 13 }{ 4 } ~~ \text{and} ~~ d = \frac{ 17 }{ 4 } $.	1
9158	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = \frac{ 13 }{ 4 } ~~ \text{and} ~~ d = \frac{ 17 }{ 4 } $.	1
9159	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 4 $.	1
9160	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	1
9161	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	1
9162	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	1
9163	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 3 $.	1
9164	Find $ S_{ 72 } $ ( sum of first $ 72 $ terms ) of arithmetic progression if $ a_1 = 1001 ~~ \text{and} ~~ d = 3 $.	1
9165	Find $ S_{ 44 } $ ( sum of first $ 44 $ terms ) of arithmetic progression if $ a_1 = 840 ~~ \text{and} ~~ d = -5 $.	1
9166	Find $ S_{ 98 } $ ( sum of first $ 98 $ terms ) of arithmetic progression if $ a_1 = -40 ~~ \text{and} ~~ d = -2 $.	1
9167	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	1
9168	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	1
9169	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	1
9170	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 3 $.	1
9171	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 115 ~~ \text{and} ~~ d = 7 $.	1
9172	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 345 ~~ \text{and} ~~ d = 30 $.	1
9173	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 36 $.	1
9174	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 36 $.	1
9175	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -35 ~~ \text{and} ~~ d = \left( -100 \right) $.	1
9176	Find $ a_{ 74 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 7 $.	1
9177	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 800 ~~ \text{and} ~~ d = 10 $.	1
9178	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 4 $.	1
9179	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 10 $.	1
9180	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 10 $.	1
9181	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = 10 $.	1
9182	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = 10 $.	1
9183	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 10 $.	1
9184	$$ a_1 = 1000 ~,~ d = 200 ~,~ S_n = 36000 ~,~ n = ? $$	1
9185	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $.	1
9186	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 0 $.	1
9187	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = 0 $.	1
9188	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 51 ~~ \text{and} ~~ d = 4 $.	1
9189	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 13 $.	1
9190	Find $ a_{ 67 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
9191	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 50 $.	1
9192	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = -4 $.	1
9193	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 0 $.	1
9194	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 17000 ~~ \text{and} ~~ d = 1250 $.	1
9195	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 17000 ~~ \text{and} ~~ d = 1250 $.	1
9196	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 17000 ~~ \text{and} ~~ d = 1250 $.	1
9197	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 17000 ~~ \text{and} ~~ d = 1250 $.	1
9198	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 17000 ~~ \text{and} ~~ d = 1250 $.	1
9199	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 57 $.	1
9200	Find $ S_{ 2022 } $ ( sum of first $ 2022 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1