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
6951	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	1
6952	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 16 $.	1
6953	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 180 ~~ \text{and} ~~ d = 10 $.	1
6954	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 180 ~~ \text{and} ~~ d = 10 $.	1
6955	Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 20 $.	1
6956	Find $ a_{ 500 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 20 $.	1
6957	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	1
6958	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 60000 ~~ \text{and} ~~ d = 3500 $.	1
6959	Find $ a_{ 99 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 12 $.	1
6960	Find $ S_{ 65 } $ ( sum of first $ 65 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 74 $.	1
6961	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 116 ~~ \text{and} ~~ d = \left( -6 \right) $.	1
6962	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	1
6963	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	1
6964	Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 2000 ~~ \text{and} ~~ d = 200 $.	1
6965	Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 2000 ~~ \text{and} ~~ d = 200 $.	1
6966	Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 20 $.	1
6967	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 1 $.	1
6968	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 1 $.	1
6969	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 8 }{ 9 } $.	1
6970	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 8 }{ 9 } $.	1
6971	Find $ S_{ 253 } $ ( sum of first $ 253 $ terms ) of arithmetic progression if $ a_1 = 2018 ~~ \text{and} ~~ d = -8 $.	1
6972	Find $ a_{ 87 } $ of an arithmetic progression if $ a_1 = 49 ~~ \text{and} ~~ d = 13 $.	1
6973	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 5 $.	1
6974	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 10 $.	1
6975	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -1 \right) $.	1
6976	Find $ a_{ 300 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
6977	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 1 $.	1
6978	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 1 $.	1
6979	Find $ a_{ 69 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 9 $.	1
6980	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 1 $.	1
6981	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 9 $.	1
6982	Find $ a_{ 91 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	1
6983	Find $ a_{ 97 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	1
6984	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \left( -1 \right) $.	1
6985	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 8 } $.	1
6986	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
6987	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	1
6988	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 412 ~~ \text{and} ~~ d = \left( -8 \right) $.	1
6989	Find $ a_{ 43 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 5 $.	1
6990	Find $ a_{ 73 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	1
6991	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = \left( -25 \right) $.	1
6992	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = -64 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
6993	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 64 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
6994	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = \frac{ 11 }{ 2 } $.	1
6995	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 5 $.	1
6996	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	1
6997	Find $ S_{ 57402 } $ ( sum of first $ 57402 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 5 $.	1
6998	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
6999	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
7000	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1