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
2801	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
2802	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
2803	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -26 ~~ \text{and} ~~ d = 200 $.	2
2804	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 67 }{ 5 } ~~ \text{and} ~~ d = \frac{ 3 }{ 5 } $.	2
2805	Find $ a_1 $ (first term of arithmetic progression) if $ d = -2 ~~ \text{and} ~~ a_{ 22 } = -44 $.	2
2806	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
2807	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = \left( -200 \right) $.	2
2808	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 5 $.	2
2809	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 9 $.	2
2810	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 200 $.	2
2811	$$ a_{ 11 } = 9 ~~,~~ S_{ 11 } = 77 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
2812	Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2
2813	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2
2814	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
2815	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 15 $.	2
2816	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 2 $.	2
2817	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 256 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 4 } \right) $.	2
2818	Find common difference $ d $ of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ a_{ 15 } = 2 $.	2
2819	Find common difference $ d $ of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ a_{ 2 } = 15 $.	2
2820	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $.	2
2821	Find $ S_{ 89 } $ ( sum of first $ 89 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $.	2
2822	Find common difference $ d $ of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ a_{ 2 } = -3 $.	2
2823	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 7 $.	2
2824	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 9 $.	2
2825	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 33 }{ 100 } ~~ \text{and} ~~ d = 0.125 $.	2
2826	Find $ S_{ 34 } $ ( sum of first $ 34 $ terms ) of arithmetic progression if $ a_1 = 88 ~~ \text{and} ~~ d = -5 $.	2
2827	Find $ a_{ 84 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = 8 $.	2
2828	Find $ a_{ 84 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = 6 $.	2
2829	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = -5 $.	2
2830	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 132 ~~ \text{and} ~~ d = -8 $.	2
2831	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 74 $.	2
2832	Find $ a_{ 95 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	2
2833	$$ a_1 = 2 ~,~ d = 3 ~,~ a_n = 299 ~,~ n = ? $$	2
2834	Find $ S_{ 250 } $ ( sum of first $ 250 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	2
2835	Find $ a_{ 44 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $.	2
2836	$$ a_1 = \frac{ 1 }{ 3 } ~,~ d = -\frac{ 1 }{ 8 } ~,~ a_n = 20 ~,~ n = ? $$	2
2837	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = 30 $.	2
2838	Find $ S_{ 130 } $ ( sum of first $ 130 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 250 $.	2
2839	$$ a_1 = -11 ~,~ d = 7 ~,~ a_n = 34 ~,~ n = ? $$	2
2840	Find $ S_{ 75 } $ ( sum of first $ 75 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	2
2841	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 9 $.	2
2842	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = \frac{ 15 }{ 8 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	2
2843	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 7 $.	2
2844	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = \frac{ 15 }{ 8 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	2
2845	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = 14 $.	2
2846	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 21 $.	2
2847	$$ a_1 = 14 ~,~ d = 21 ~,~ a_n = \frac{ 3 }{ 2 } ~,~ n = ? $$	2
2848	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 1250 ~~ \text{and} ~~ d = 150 $.	2
2849	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 1250 ~~ \text{and} ~~ d = \left( -150 \right) $.	2
2850	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 1250 ~~ \text{and} ~~ d = \left( -150 \right) $.	2