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
6001	Find $ a_{ 89 } $ of an arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 0 $.	2
6002	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
6003	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
6004	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 500 $.	2
6005	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 49 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
6006	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 670000 ~~ \text{and} ~~ d = 100000 $.	2
6007	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 6700000 ~~ \text{and} ~~ d = 100000 $.	2
6008	$$ a_1 = 5 ~,~ d = 7 ~,~ S_n = 138 ~,~ n = ? $$	2
6009	Find $ a_{ 83 } $ of an arithmetic progression if $ a_1 = -26 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
6010	$$ a_1 = \frac{ 1 }{ 5 } ~,~ d = \frac{ 53 }{ 100 } ~,~ a_n = 25 ~,~ n = ? $$	2
6011	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	2
6012	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	2
6013	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	2
6014	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	2
6015	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	2
6016	$$ a_1 = 7 ~,~ d = -4 ~,~ a_n = 11 ~,~ n = ? $$	2
6017	Find $ a_1 $ (first term of arithmetic progression) if $ d = 6 ~~ \text{and} ~~ a_{ 101 } = 596 $.	2
6018	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 6 $.	2
6019	$$ a_1 = -4 ~,~ d = 6 ~,~ S_n = 230 ~,~ n = ? $$	2
6020	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $.	2
6021	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
6022	Find $ a_{ 61 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
6023	Find $ S_{ 101 } $ ( sum of first $ 101 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	2
6024	Find $ S_{ 98 } $ ( sum of first $ 98 $ terms ) of arithmetic progression if $ a_1 = 881 ~~ \text{and} ~~ d = -9 $.	2
6025	Find $ S_{ 1 } $ ( sum of first $ 1 $ terms ) of arithmetic progression if $ a_1 = 9245 ~~ \text{and} ~~ d = 5736 $.	2
6026	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 9245 ~~ \text{and} ~~ d = 5736 $.	2
6027	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 9245 ~~ \text{and} ~~ d = 5429 $.	2
6028	Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 9245 ~~ \text{and} ~~ d = 5736 $.	2
6029	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 16 $.	2
6030	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
6031	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 6 $.	2
6032	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 50 $.	2
6033	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = -4 $.	2
6034	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 3 $.	2
6035	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = \left( -9 \right) $.	2
6036	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = \left( -9 \right) $.	2
6037	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 3750 ~~ \text{and} ~~ d = 5 $.	2
6038	Find $ S_{ 29 } $ ( sum of first $ 29 $ terms ) of arithmetic progression if $ a_1 = 41 ~~ \text{and} ~~ d = -3 $.	2
6039	Find $ a_{ 76 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 2 $.	2
6040	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
6041	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	2
6042	Find $ a_{ 998 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
6043	Find $ S_{ 999 } $ ( sum of first $ 999 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
6044	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 2 $.	2
6045	$$ a_1 = 9 ~,~ d = -3 ~,~ a_n = -342 ~,~ n = ? $$	2
6046	Find $ S_{ 118 } $ ( sum of first $ 118 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = -3 $.	2
6047	Find $ S_{ 111 } $ ( sum of first $ 111 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = -4 $.	2
6048	$$ a_1 = 3 ~,~ d = 3 ~,~ a_n = 348 ~,~ n = ? $$	2
6049	Find $ S_{ 116 } $ ( sum of first $ 116 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
6050	Find $ S_{ 78 } $ ( sum of first $ 78 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 2 $.	2