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
2651	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 3 $.	3
2652	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 2 $.	3
2653	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 2 $.	3
2654	$$ a_1 = 16 ~~,~~ d = 9 ~~,~~ a_1 = ? ~~,~~ d = ? $$	3
2655	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 6 $.	3
2656	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 8600000 ~~ \text{and} ~~ d = 200000 $.	2
2657	Find $ S_{ 65 } $ ( sum of first $ 65 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 3 $.	2
2658	Find $ a_{ 365 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ d = \frac{ 1 }{ 10 } $.	2
2659	$$ a_1 = \frac{ 1 }{ 10 } ~,~ d = \frac{ 1 }{ 10 } ~,~ a_n = 1000 ~,~ n = ? $$	2
2660	$$ a_1 = \frac{ 1 }{ 10 } ~,~ d = \frac{ 1 }{ 10 } ~,~ S_n = 1000 ~,~ n = ? $$	2
2661	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 15 $.	2
2662	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 30 $.	2
2663	Find $ a_1 $ (first term of arithmetic progression) if $ d = -38 ~~ \text{and} ~~ a_{ 6 } = 2 $.	2
2664	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 5 $.	2
2665	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
2666	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 10 $.	2
2667	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = -3 $.	2
2668	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	2
2669	$$ a_1 = 5 ~,~ d = 3 ~,~ S_n = 55 ~,~ n = ? $$	2
2670	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
2671	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = -4 $.	2
2672	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	2
2673	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = 8 $.	2
2674	Find $ a_{ 500 } $ of an arithmetic progression if $ a_1 = 1050 ~~ \text{and} ~~ d = 105 $.	2
2675	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
2676	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 5 $.	2
2677	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 7 $.	2
2678	Find $ a_{ 89 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 5 $.	2
2679	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 20 $.	2
2680	Find $ S_{ 27 } $ ( sum of first $ 27 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 15 $.	2
2681	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 9 $.	2
2682	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	2
2683	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	2
2684	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	2
2685	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	2
2686	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	2
2687	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	2
2688	Find $ a_{ 1232 } $ of an arithmetic progression if $ a_1 = -91 ~~ \text{and} ~~ d = 179 $.	2
2689	Find $ a_{ 1232 } $ of an arithmetic progression if $ a_1 = -91 ~~ \text{and} ~~ d = 0 $.	2
2690	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = -91 ~~ \text{and} ~~ d = 0 $.	2
2691	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 1232 ~~ \text{and} ~~ d = \left( -91 \right) $.	2
2692	Find $ S_{ 101 } $ ( sum of first $ 101 $ terms ) of arithmetic progression if $ a_1 = 80 ~~ \text{and} ~~ d = 8 $.	2
2693	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 64 ~~ \text{and} ~~ d = 1660 $.	2
2694	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 86 ~~ \text{and} ~~ d = 15 $.	2
2695	Find $ S_{ 55 } $ ( sum of first $ 55 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 7 $.	2
2696	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 112 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
2697	Find common difference $ d $ of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ a_{ 25 } = -12 $.	2
2698	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	2
2699	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	2
2700	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 5 $.	2