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
6551	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 20 $.	1
6552	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 45 ~~ \text{and} ~~ d = 45 $.	1
6553	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -\frac{ 3 }{ 5 } ~~ \text{and} ~~ d = 1 $.	1
6554	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = \frac{ 79 }{ 10 } ~~ \text{and} ~~ d = \left( -\frac{ 8 }{ 5 } \right) $.	1
6555	$$ a_1 = 15 ~,~ a_n = 51 ~,~ S_n = 429 ~,~ n = ? $$	1
6556	Find $ a_1 $ (first term of arithmetic progression) if $ d = 7 ~~ \text{and} ~~ S_{ 1938 } = 1938 $.	1
6557	Find $ a_1 $ (first term of arithmetic progression) if $ d = -13 ~~ \text{and} ~~ S_{ 9 } = -549 $.	1
6558	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
6559	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
6560	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = -20 $.	1
6561	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = -17 $.	1
6562	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = \left( -14 \right) $.	1
6563	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = -12 $.	1
6564	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = -9 $.	1
6565	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = \left( -9 \right) $.	1
6566	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 92 ~~ \text{and} ~~ d = \left( -10 \right) $.	1
6567	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 137 ~~ \text{and} ~~ d = -11 $.	1
6568	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 137 ~~ \text{and} ~~ d = -11 $.	1
6569	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 137 ~~ \text{and} ~~ d = -11 $.	1
6570	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 115 ~~ \text{and} ~~ d = -8 $.	1
6571	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 129 ~~ \text{and} ~~ d = -8 $.	1
6572	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 129 ~~ \text{and} ~~ d = -8 $.	1
6573	Find $ S_{ 42 } $ ( sum of first $ 42 $ terms ) of arithmetic progression if $ a_1 = 620 ~~ \text{and} ~~ d = 5 $.	1
6574	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 14 $.	1
6575	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 5 $.	1
6576	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 73 ~~ \text{and} ~~ d = 10 $.	1
6577	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 73 ~~ \text{and} ~~ d = -8 $.	1
6578	Find $ a_{ 61 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 6 $.	1
6579	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 61 ~~ \text{and} ~~ d = 24 $.	1
6580	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = -31 ~~ \text{and} ~~ d = -9 $.	1
6581	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 4 $.	1
6582	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 5 $.	1
6583	Find $ S_{ 94 } $ ( sum of first $ 94 $ terms ) of arithmetic progression if $ a_1 = 94 ~~ \text{and} ~~ d = 0 $.	1
6584	Find $ a_{ 94 } $ of an arithmetic progression if $ a_1 = 94 ~~ \text{and} ~~ d = \left( -1 \right) $.	1
6585	Find $ d $ (common difference of arithmetic progression) if $ a_1 = \frac{ 5 }{ 3 } ~~ \text{and} ~~ S_{ 26 } = \frac{ 91 }{ 3 } $.	1
6586	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 3 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 25 } \right) $.	1
6587	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = \left( -10 \right) $.	1
6588	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = 2 $.	1
6589	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -29 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
6590	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -6 \right) $.	1
6591	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 7 $.	1
6592	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
6593	Find $ a_{ 120 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
6594	$$ a_{ 9 } = 15 ~~,~~ S_{ 21 } = 51 ~~,~~ a_1 = ? ~~,~~ d = ? $$	1
6595	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -36 ~~ \text{and} ~~ d = 20 $.	1
6596	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 20 $.	1
6597	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 20 $.	1
6598	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 17 $.	1
6599	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 8 $.	1
6600	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 6200 ~~ \text{and} ~~ d = \left( -500 \right) $.	1