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
2701	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	2
2702	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 5 $.	2
2703	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 8 $.	2
2704	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 10 $.	2
2705	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 10 $.	2
2706	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 4 $.	2
2707	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 6 $.	2
2708	$$ a_1 = \frac{ 1 }{ 2 } ~~,~~ d = \frac{ 1 }{ 2 } ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
2709	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 5 $.	2
2710	$$ a_1 = 57 ~,~ a_n = 32 ~,~ S_n = -1152 ~,~ n = ? $$	2
2711	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 4 $.	2
2712	Find $ S_{ 55 } $ ( sum of first $ 55 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	2
2713	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
2714	$$ a_1 = 8 ~,~ a_n = 113 ~,~ S_n = 968 ~,~ n = ? $$	2
2715	$$ a_1 = 1 ~,~ d = -7 ~,~ a_n = -27 ~,~ n = ? $$	2
2716	Find $ a_{ 43 } $ of an arithmetic progression if $ a_1 = 352 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
2717	$$ a_1 = 31 ~,~ d = 5 ~,~ a_n = 53 ~,~ n = ? $$	2
2718	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 53 ~~ \text{and} ~~ d = 5 $.	2
2719	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 1725 ~~ \text{and} ~~ d = 35 $.	2
2720	Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 1 $.	2
2721	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = -6 $.	2
2722	Find $ a_{ 123 } $ of an arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = 300 $.	2
2723	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 310 ~~ \text{and} ~~ d = 10 $.	2
2724	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	2
2725	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	2
2726	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 92 ~~ \text{and} ~~ d = 1 $.	2
2727	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 7 $.	2
2728	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 39 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
2729	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
2730	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
2731	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 8000 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	2
2732	Find $ a_{ 59 } $ of an arithmetic progression if $ a_1 = 63 ~~ \text{and} ~~ d = 67 $.	2
2733	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
2734	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 9 $.	2
2735	$$ a_1 = -17 ~,~ d = 1 ~,~ a_n = 72 ~,~ n = ? $$	2
2736	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 25 $.	2
2737	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = 77 $.	2
2738	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 5 $.	2
2739	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -\frac{ 7 }{ 9 } \right) $.	2
2740	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 4 $.	2
2741	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 10 $.	2
2742	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 7 $.	2
2743	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 2 $.	2
2744	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 2 $.	2
2745	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
2746	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 3800 ~~ \text{and} ~~ d = 105 $.	2
2747	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
2748	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	2
2749	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	2
2750	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 0 $.	2