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
2551	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \left( -2 \right) $.	3
2552	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = -2 $.	3
2553	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 39 }{ 2 } ~~ \text{and} ~~ d = 3 $.	3
2554	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	3
2555	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 20 $.	3
2556	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 20 $.	3
2557	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 7 $.	3
2558	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 9 $.	3
2559	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 5 $.	3
2560	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -\frac{ 94 }{ 3 } ~~ \text{and} ~~ d = \left( -\frac{ 13 }{ 3 } \right) $.	3
2561	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	3
2562	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -4 \right) $.	3
2563	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 510 ~~ \text{and} ~~ d = 5 $.	3
2564	Find $ S_{ 41 } $ ( sum of first $ 41 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	3
2565	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 89 ~~ \text{and} ~~ d = \frac{ 11 }{ 10 } $.	3
2566	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 2 $.	3
2567	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	3
2568	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 3 $.	3
2569	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -2 \right) $.	3
2570	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 15000 ~~ \text{and} ~~ d = 500 $.	3
2571	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 15000 ~~ \text{and} ~~ d = 500 $.	3
2572	Find $ a_{ 120 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	3
2573	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	3
2574	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 41 ~~ \text{and} ~~ d = 1 $.	3
2575	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 70 ~~ \text{and} ~~ d = 1 $.	3
2576	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 69 ~~ \text{and} ~~ d = 1 $.	3
2577	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	3
2578	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 7 $.	3
2579	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = 4 $.	3
2580	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 5 $.	3
2581	Find $ a_1 $ (first term of arithmetic progression) if $ d = \frac{ 29 }{ 4 } ~~ \text{and} ~~ a_{ 83 } = -\frac{ 203 }{ 2 } $.	3
2582	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 0 $.	3
2583	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = -32 ~~ \text{and} ~~ d = 20 $.	3
2584	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	3
2585	$$ a_1 = 1 ~,~ d = 4 ~,~ S_n = 91 ~,~ n = ? $$	3
2586	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -100 ~~ \text{and} ~~ d = 8 $.	3
2587	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = -100 ~~ \text{and} ~~ d = 8 $.	3
2588	Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	3
2589	Find $ S_{ 54 } $ ( sum of first $ 54 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 7 $.	3
2590	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	3
2591	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	3
2592	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 31 ~~ \text{and} ~~ d = 5 $.	3
2593	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	3
2594	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 39 ~~ \text{and} ~~ d = \left( -8 \right) $.	3
2595	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	3
2596	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = \left( -8 \right) $.	3
2597	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -\frac{ 1 }{ 49 } ~~ \text{and} ~~ d = \left( -7 \right) $.	3
2598	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 54 ~~ \text{and} ~~ d = 1 $.	3
2599	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	3
2600	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 14 $.	3