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
7551	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 5000 $.	1
7552	Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 5000 $.	1
7553	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -22 ~~ \text{and} ~~ d = 4 $.	1
7554	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 3 $.	1
7555	Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	1
7556	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = \frac{ 44 }{ 5 } ~~ \text{and} ~~ d = \frac{ 13 }{ 5 } $.	1
7557	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
7558	Find $ S_{ 1010 } $ ( sum of first $ 1010 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	1
7559	Find $ a_{ 81 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 6 $.	1
7560	Find $ S_{ 8192 } $ ( sum of first $ 8192 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
7561	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	1
7562	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $.	1
7563	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	1
7564	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 30 $.	1
7565	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = 60 $.	1
7566	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = -1 $.	1
7567	Find common difference $ d $ of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ a_{ 4 } = 13.82 $.	1
7568	$$ a_1 = 11 ~,~ a_n = 195 ~,~ S_n = 2472 ~,~ n = ? $$	1
7569	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 599 ~~ \text{and} ~~ d = -6 $.	1
7570	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 6 $.	1
7571	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
7572	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 131 }{ 10 } ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	1
7573	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 131 }{ 10 } ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	1
7574	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = -\frac{ 7 }{ 6 } $.	1
7575	Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 8 $.	1
7576	Find $ S_{ 108 } $ ( sum of first $ 108 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	1
7577	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	1
7578	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $.	1
7579	Find $ S_{ 300 } $ ( sum of first $ 300 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	1
7580	Find $ a_{ 491 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 6 $.	1
7581	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 6 $.	1
7582	$$ a_1 = 11 ~,~ d = 6 ~,~ a_n = 491 ~,~ n = ? $$	1
7583	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 10 $.	1
7584	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	1
7585	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 3 $.	1
7586	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 25 $.	1
7587	Find $ a_{ 318 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	1
7588	Find $ a_{ 138 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	1
7589	Find $ S_{ 138 } $ ( sum of first $ 138 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	1
7590	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = -6 $.	1
7591	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -\frac{ 8 }{ 5 } \right) $.	1
7592	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 40000 ~~ \text{and} ~~ d = 3000 $.	1
7593	Find $ S_{ 180 } $ ( sum of first $ 180 $ terms ) of arithmetic progression if $ a_1 = 200000 ~~ \text{and} ~~ d = -1111 $.	1
7594	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 3 $.	1
7595	Find $ a_{ 407 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 3 $.	1
7596	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 5 }{ 8 } $.	1
7597	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	1
7598	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 27 } ~~ \text{and} ~~ d = 3 $.	1
7599	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	1
7600	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	1