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
4001	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = -1 $.	2
4002	Find $ a_{ 65 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 9 $.	2
4003	Find $ a_{ 273 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 3 $.	2
4004	Find $ S_{ 79 } $ ( sum of first $ 79 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 7 $.	2
4005	Find $ S_{ 61 } $ ( sum of first $ 61 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 6 $.	2
4006	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 0 $.	2
4007	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 6 $.	2
4008	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ d = \left( -3 \right) $.	2
4009	Find $ S_{ 44 } $ ( sum of first $ 44 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 1 $.	2
4010	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 120 ~~ \text{and} ~~ d = -20 $.	2
4011	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ d = \left( -2 \right) $.	2
4012	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 56000 ~~ \text{and} ~~ d = 610 $.	2
4013	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 56000 ~~ \text{and} ~~ d = 610 $.	2
4014	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = -21 ~~ \text{and} ~~ d = \frac{ 3 }{ 5 } $.	2
4015	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 9 $.	2
4016	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 8 $.	2
4017	Find $ S_{ 700 } $ ( sum of first $ 700 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4018	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 7 $.	2
4019	Find $ S_{ 1234 } $ ( sum of first $ 1234 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	2
4020	Find common difference $ d $ of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ a_{ 15 } = 37 $.	2
4021	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2
4022	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 1 $.	2
4023	Find $ S_{ 1234 } $ ( sum of first $ 1234 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
4024	$$ a_{ 15 } = -5 ~~,~~ S_{ 36 } = 180 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
4025	$$ a_{ 2 } = 2 ~~,~~ S_{ 34 } = 3 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
4026	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	2
4027	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	2
4028	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
4029	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = -9 $.	2
4030	Find $ S_{ 89 } $ ( sum of first $ 89 $ terms ) of arithmetic progression if $ a_1 = -40 ~~ \text{and} ~~ d = -2 $.	2
4031	Find $ S_{ 98 } $ ( sum of first $ 98 $ terms ) of arithmetic progression if $ a_1 = -40 ~~ \text{and} ~~ d = 2 $.	2
4032	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 1 $.	2
4033	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 1 $.	2
4034	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = -652 ~~ \text{and} ~~ d = \left( -30 \right) $.	2
4035	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 15 $.	2
4036	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = \left( -43 \right) $.	2
4037	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 4 $.	2
4038	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 4 $.	2
4039	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 4 $.	2
4040	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 4 $.	2
4041	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 800 ~~ \text{and} ~~ d = 10 $.	2
4042	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 200 $.	2
4043	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 3 $.	2
4044	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 115 ~~ \text{and} ~~ d = 7 $.	2
4045	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 0 $.	2
4046	$$ a_1 = 4 ~,~ d = 7 ~,~ S_n = 228 ~,~ n = ? $$	2
4047	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 8 $.	2
4048	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 9 $.	2
4049	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 28 $.	2
4050	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 28 $.	2