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
5451	Find $ S_{ 43 } $ ( sum of first $ 43 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	2
5452	Find $ S_{ 7000 } $ ( sum of first $ 7000 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	2
5453	$$ a_1 = -20 ~,~ d = 4 ~,~ a_n = 16 ~,~ n = ? $$	2
5454	Find common difference $ d $ of arithmetic progression if $ a_1 = 10000000 ~~ \text{and} ~~ a_{ 5 } = 15000000 $.	2
5455	Find common difference $ d $ of arithmetic progression if $ a_1 = 10000000 ~~ \text{and} ~~ a_{ 2 } = 15000000 $.	2
5456	Find $ S_{ 39 } $ ( sum of first $ 39 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	2
5457	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
5458	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = \frac{ 11 }{ 5 } ~~ \text{and} ~~ d = \frac{ 11 }{ 10 } $.	2
5459	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 365 ~~ \text{and} ~~ d = 1 $.	2
5460	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
5461	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
5462	$$ a_1 = 5 ~,~ d = 7 ~,~ S_n = 670 ~,~ n = ? $$	2
5463	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5464	Find $ S_{ 65 } $ ( sum of first $ 65 $ terms ) of arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = 1 $.	2
5465	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = 1 $.	2
5466	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 330 ~~ \text{and} ~~ d = 1 $.	2
5467	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 4 $.	2
5468	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 0 $.	2
5469	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 5 $.	2
5470	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -\frac{ 3 }{ 2 } \right) $.	2
5471	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = 7 $.	2
5472	Find $ a_{ 111 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = 7 $.	2
5473	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 6 $.	2
5474	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -9 \right) $.	2
5475	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
5476	Find $ a_{ 1234 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5477	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
5478	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5479	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 4 $.	2
5480	Find $ S_{ 139 } $ ( sum of first $ 139 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $.	2
5481	$$ a_1 = 1 ~,~ d = 1 ~,~ S_n = 78 ~,~ n = ? $$	2
5482	$$ a_1 = 3 ~,~ d = 4 ~,~ S_n = 1830 ~,~ n = ? $$	2
5483	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	2
5484	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	2
5485	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	2
5486	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = \frac{ 81 }{ 5 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 5 } \right) $.	2
5487	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 6 $.	2
5488	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 1 $.	2
5489	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 0 $.	2
5490	$$ a_1 = 6 ~,~ d = -1 ~,~ S_n = -570 ~,~ n = ? $$	2
5491	$$ a_1 = 6 ~,~ d = -1 ~,~ S_n = -326 ~,~ n = ? $$	2
5492	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 4 $.	2
5493	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = 4 $.	2
5494	Find $ a_{ 54 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 9 $.	2
5495	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 0 $.	2
5496	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 31 ~~ \text{and} ~~ d = -8 $.	2
5497	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 59 ~~ \text{and} ~~ d = 5 $.	2
5498	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 8 $.	2
5499	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = -24 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
5500	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	2