Arithmetic sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Arithmetic sequences.

Select category

ID	Problem	Count
2501	Find $ a_{ 64 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	3
2502	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	3
2503	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	3
2504	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 3 $.	3
2505	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 101 ~~ \text{and} ~~ d = 9 $.	3
2506	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	3
2507	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	3
2508	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	3
2509	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 3 $.	3
2510	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = -4 $.	3
2511	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 7 $.	3
2512	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 27000 ~~ \text{and} ~~ d = 700 $.	3
2513	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = -4 $.	3
2514	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 6 $.	3
2515	Find $ a_{ 101 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 6 $.	3
2516	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 6 $.	3
2517	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 2000 ~~ \text{and} ~~ d = 1 $.	3
2518	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	3
2519	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 3 $.	3
2520	Find $ a_{ 91 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	3
2521	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = 5 $.	3
2522	Find $ a_{ 86 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = \left( -6 \right) $.	3
2523	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 7 $.	3
2524	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 12 $.	3
2525	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 1 $.	3
2526	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 5 $.	3
2527	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = 1 $.	3
2528	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 20000 ~~ \text{and} ~~ d = 1750 $.	3
2529	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	3
2530	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 648 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	3
2531	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -\frac{ 27 }{ 5 } ~~ \text{and} ~~ d = \left( -\frac{ 6 }{ 5 } \right) $.	3
2532	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 34 $.	3
2533	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	3
2534	$$ a_1 = 15 ~,~ a_n = 99 ~,~ S_n = 3249 ~,~ n = ? $$	3
2535	Find $ S_{ 4392 } $ ( sum of first $ 4392 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 20 $.	3
2536	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 4 $.	3
2537	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \left( -4 \right) $.	3
2538	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 2 $.	3
2539	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 1409 }{ 50 } ~~ \text{and} ~~ d = \frac{ 1409 }{ 50 } $.	3
2540	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 29 $.	3
2541	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 6 $.	3
2542	Find $ a_{ 55 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 10 $.	3
2543	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 5 $.	3
2544	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	3
2545	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 4 $.	3
2546	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $.	3
2547	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -4 \right) $.	3
2548	Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ a_{ 50 } = 199 $.	3
2549	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = -13 $.	3
2550	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 2 $.	3