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
3001	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 8 $.	2
3002	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	2
3003	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	2
3004	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 23 }{ 10 } ~~ \text{and} ~~ d = \left( -\frac{ 4 }{ 5 } \right) $.	2
3005	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	2
3006	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 10 $.	2
3007	Find $ a_{ 34750 } $ of an arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 450 $.	2
3008	Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 450 $.	2
3009	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 2800 ~~ \text{and} ~~ d = 280 $.	2
3010	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 2800 ~~ \text{and} ~~ d = 280 $.	2
3011	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ d = -\frac{ 1 }{ 2 } $.	2
3012	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
3013	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = 52 $.	2
3014	$$ a_1 = 126 ~,~ d = 30 ~,~ a_n = 996 ~,~ n = ? $$	2
3015	Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = \left( -40 \right) $.	2
3016	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = \frac{ 9 }{ 17 } $.	2
3017	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 3 }{ 10 } $.	2
3018	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = -127 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
3019	Find $ S_{ 365 } $ ( sum of first $ 365 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 3 $.	2
3020	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = \left( -1 \right) $.	2
3021	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = -26 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
3022	Find $ a_{ 53 } $ of an arithmetic progression if $ a_1 = 27 ~~ \text{and} ~~ d = 16 $.	2
3023	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	2
3024	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 5 $.	2
3025	Find $ a_{ 78 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 9 $.	2
3026	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 3 $.	2
3027	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 7 $.	2
3028	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \frac{ 29 }{ 20 } $.	2
3029	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 53 ~~ \text{and} ~~ d = 6 $.	2
3030	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = -1 $.	2
3031	Find common difference $ d $ of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ a_{ 5 } = 243 $.	2
3032	Find common difference $ d $ of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ a_{ 5 } = 243 $.	2
3033	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -1 \right) $.	2
3034	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = 2 $.	2
3035	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 84 ~~ \text{and} ~~ d = 4 $.	2
3036	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -1 \right) $.	2
3037	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = -\frac{ 5 }{ 18 } $.	2
3038	$$ a_1 = 9 ~~,~~ d = 23 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
3039	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 3 $.	2
3040	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -\frac{ 11 }{ 3 } ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $.	2
3041	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -\frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 4 } \right) $.	2
3042	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 250 ~~ \text{and} ~~ d = 25 $.	2
3043	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	2
3044	Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 4841 ~~ \text{and} ~~ d = 41 $.	2
3045	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 0 $.	2
3046	Find $ a_{ 180 } $ of an arithmetic progression if $ a_1 = 10000 ~~ \text{and} ~~ d = 10000 $.	2
3047	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ d = \frac{ 1 }{ 10 } $.	2
3048	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ d = \frac{ 1 }{ 10 } $.	2
3049	Find $ a_{ 190 } $ of an arithmetic progression if $ a_1 = 72 ~~ \text{and} ~~ d = 1 $.	2
3050	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 15 }{ 2 } $.	2