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
2401	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -3 \right) $.	3
2402	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -5 \right) $.	3
2403	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 0 $.	3
2404	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $.	3
2405	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	3
2406	Find $ S_{ 1 } $ ( sum of first $ 1 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	3
2407	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 74 ~~ \text{and} ~~ d = 17 $.	3
2408	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \left( -2 \right) $.	3
2409	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 399 }{ 100 } ~~ \text{and} ~~ d = \frac{ 439 }{ 100 } $.	3
2410	Find $ a_{ 87 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 6 $.	3
2411	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 3 $.	3
2412	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 2 $.	3
2413	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \left( -9 \right) $.	3
2414	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	3
2415	Find $ S_{ 99 } $ ( sum of first $ 99 $ terms ) of arithmetic progression if $ a_1 = 49 ~~ \text{and} ~~ d = 45 $.	3
2416	Find $ S_{ 49 } $ ( sum of first $ 49 $ terms ) of arithmetic progression if $ a_1 = 99 ~~ \text{and} ~~ d = 45 $.	3
2417	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	3
2418	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 67 ~~ \text{and} ~~ d = \left( -30 \right) $.	3
2419	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = \frac{ 173 }{ 50 } ~~ \text{and} ~~ d = \frac{ 27 }{ 100 } $.	3
2420	Find $ S_{ 60000 } $ ( sum of first $ 60000 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	3
2421	Find $ a_{ 65536 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	3
2422	Find $ S_{ 65 } $ ( sum of first $ 65 $ terms ) of arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = 83 $.	3
2423	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	3
2424	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 3 $.	3
2425	Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 88 $.	3
2426	Find $ S_{ 88 } $ ( sum of first $ 88 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 1 $.	3
2427	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 28 $.	3
2428	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 28 $.	3
2429	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	3
2430	Find $ S_{ 75 } $ ( sum of first $ 75 $ terms ) of arithmetic progression if $ a_1 = 79 ~~ \text{and} ~~ d = 91 $.	3
2431	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = \left( -6 \right) $.	3
2432	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = -4 $.	3
2433	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 3 $.	3
2434	Find $ a_{ 94 } $ of an arithmetic progression if $ a_1 = -26 ~~ \text{and} ~~ d = \left( -11 \right) $.	3
2435	Find $ a_{ 55 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 2 $.	3
2436	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	3
2437	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 50 $.	3
2438	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	3
2439	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = 9 $.	3
2440	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -6 \right) $.	3
2441	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	3
2442	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = -22 ~~ \text{and} ~~ d = 7 $.	3
2443	$$ a_1 = 1 ~,~ d = 1 ~,~ S_n = 120 ~,~ n = ? $$	3
2444	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	3
2445	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 0 $.	3
2446	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 4 $.	3
2447	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = -23 ~~ \text{and} ~~ d = 2 $.	3
2448	$$ a_1 = 12 ~,~ d = 3 ~,~ a_n = 312 ~,~ n = ? $$	3
2449	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	3
2450	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 9 $.	3