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
8951	Find $ S_{ 114 } $ ( sum of first $ 114 $ terms ) of arithmetic progression if $ a_1 = 900 ~~ \text{and} ~~ d = 20 $.	1
8952	Find $ S_{ 114 } $ ( sum of first $ 114 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 20 $.	1
8953	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 1 $.	1
8954	Find $ S_{ 164 } $ ( sum of first $ 164 $ terms ) of arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = 1 $.	1
8955	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 2 $.	1
8956	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 9 $.	1
8957	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 49 ~~ \text{and} ~~ d = 3 $.	1
8958	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 9 $.	1
8959	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 48500 ~~ \text{and} ~~ d = 1200 $.	1
8960	Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 106 ~~ \text{and} ~~ d = -3 $.	1
8961	$$ a_{ 8 } = -9 ~~,~~ S_{ 5 } = 30 ~~,~~ a_1 = ? ~~,~~ d = ? $$	1
8962	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 13 $.	1
8963	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 13 $.	1
8964	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 9 $.	1
8965	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 9 $.	1
8966	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 9 $.	1
8967	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 9 $.	1
8968	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 9 $.	1
8969	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 9 $.	1
8970	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 9 $.	1
8971	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
8972	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
8973	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
8974	Find $ a_{ 55 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
8975	Find $ a_{ 54 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
8976	Find $ a_{ 53 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
8977	Find $ a_{ 49 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
8978	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 2 $.	1
8979	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 7 $.	1
8980	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = \left( -100 \right) $.	1
8981	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 49 ~~ \text{and} ~~ d = 2 $.	1
8982	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 121 ~~ \text{and} ~~ d = -4 $.	1
8983	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
8984	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
8985	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
8986	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
8987	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $.	1
8988	Find $ S_{ 99 } $ ( sum of first $ 99 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = -10 $.	1
8989	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 0 $.	1
8990	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = \frac{ 16 }{ 5 } ~~ \text{and} ~~ d = -\frac{ 3 }{ 10 } $.	1
8991	Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ a_{ 14 } = 207 $.	1
8992	Find $ a_{ 42 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 7 $.	1
8993	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	1
8994	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = \left( -16 \right) $.	1
8995	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = \left( -12 \right) $.	1
8996	Find $ a_{ 58 } $ of an arithmetic progression if $ a_1 = -125 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
8997	Find $ a_{ 58 } $ of an arithmetic progression if $ a_1 = -125 ~~ \text{and} ~~ d = 5 $.	1
8998	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	1
8999	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	1
9000	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = -4 $.	1