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
2851	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 1250 ~~ \text{and} ~~ d = \left( -150 \right) $.	2
2852	Find $ a_{ 51 } $ of an arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
2853	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 27 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
2854	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = 10 $.	2
2855	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 7 $.	2
2856	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 9 $.	2
2857	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 6 $.	2
2858	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 6 $.	2
2859	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -\frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 5 }{ 3 } $.	2
2860	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	2
2861	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	2
2862	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = 4 $.	2
2863	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 17 }{ 5 } ~~ \text{and} ~~ d = \frac{ 17 }{ 10 } $.	2
2864	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = \frac{ 17 }{ 5 } ~~ \text{and} ~~ d = \frac{ 17 }{ 10 } $.	2
2865	Find $ a_{ 42 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 0 $.	2
2866	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 9 $.	2
2867	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
2868	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = -28 ~~ \text{and} ~~ d = 6 $.	2
2869	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
2870	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
2871	Find $ a_{ 49 } $ of an arithmetic progression if $ a_1 = -52 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
2872	Find $ S_{ 41 } $ ( sum of first $ 41 $ terms ) of arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = 5 $.	2
2873	$$ a_1 = 3 ~~,~~ d = 9 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
2874	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	2
2875	Find $ S_{ 93 } $ ( sum of first $ 93 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
2876	Find $ S_{ 91 } $ ( sum of first $ 91 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 91 $.	2
2877	Find $ S_{ 99 } $ ( sum of first $ 99 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 1 $.	2
2878	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 6 $.	2
2879	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 9 $.	2
2880	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = 8 $.	2
2881	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	2
2882	$$ a_1 = 3 ~,~ d = 33 ~,~ S_n = 3 ~,~ n = ? $$	2
2883	Find $ S_{ 71 } $ ( sum of first $ 71 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 40 $.	2
2884	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 79 $.	2
2885	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 5 $.	2
2886	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = -\frac{ 5 }{ 8 } $.	2
2887	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = \frac{ 7 }{ 5 } ~~ \text{and} ~~ d = \frac{ 3 }{ 5 } $.	2
2888	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	2
2889	Find $ a_{ 210 } $ of an arithmetic progression if $ a_1 = 115 ~~ \text{and} ~~ d = 80 $.	2
2890	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 115 ~~ \text{and} ~~ d = 80 $.	2
2891	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 225 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
2892	Find $ a_{ 500 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 3 $.	2
2893	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
2894	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 1725 ~~ \text{and} ~~ d = -1 $.	2
2895	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = -1 $.	2
2896	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = -1 $.	2
2897	$$ a_1 = 43 ~,~ d = 10 ~,~ a_n = 433 ~,~ n = ? $$	2
2898	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -32 ~~ \text{and} ~~ d = 3 $.	2
2899	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
2900	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	2