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
5501	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 160 ~~ \text{and} ~~ d = 0 $.	2
5502	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = \frac{ 43 }{ 2 } ~~ \text{and} ~~ d = \frac{ 43 }{ 2 } $.	2
5503	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = \frac{ 43 }{ 2 } ~~ \text{and} ~~ d = \frac{ 43 }{ 2 } $.	2
5504	Find $ a_{ 49 } $ of an arithmetic progression if $ a_1 = \frac{ 445 }{ 4 } ~~ \text{and} ~~ d = \frac{ 25 }{ 4 } $.	2
5505	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = \frac{ 445 }{ 4 } ~~ \text{and} ~~ d = \frac{ 25 }{ 4 } $.	2
5506	Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	2
5507	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 3 $.	2
5508	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	2
5509	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	2
5510	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
5511	Find $ a_{ 3500 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 11 $.	2
5512	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5513	Find $ a_{ 90 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 40 $.	2
5514	$$ a_1 = 19 ~,~ d = -4 ~,~ S_n = -441 ~,~ n = ? $$	2
5515	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 4567 ~~ \text{and} ~~ d = \left( -1111 \right) $.	2
5516	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 20 $.	2
5517	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 58 ~~ \text{and} ~~ d = 7 $.	2
5518	$$ a_1 = 12 ~,~ d = 0 ~,~ a_n = 0 ~,~ n = ? $$	2
5519	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 0 $.	2
5520	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 24 $.	2
5521	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 960 ~~ \text{and} ~~ d = 160 $.	2
5522	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
5523	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = 3 $.	2
5524	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
5525	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
5526	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -\frac{ 3 }{ 2 } \right) $.	2
5527	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 305 ~~ \text{and} ~~ d = \left( -9 \right) $.	2
5528	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ d = 5 $.	2
5529	$$ a_1 = 51 ~,~ d = 22 ~,~ a_n = 1 ~,~ n = ? $$	2
5530	$$ a_1 = 51 ~,~ d = 12 ~,~ a_n = 0 ~,~ n = ? $$	2
5531	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = \frac{ 20 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
5532	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = -5 $.	2
5533	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 70 $.	2
5534	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 8 $.	2
5535	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = -2 $.	2
5536	Find $ a_{ 42 } $ of an arithmetic progression if $ a_1 = 99 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
5537	Find $ a_1 $ (first term of arithmetic progression) if $ d = 7 ~~ \text{and} ~~ a_{ 8 } = 43 $.	2
5538	Find $ S_{ 102 } $ ( sum of first $ 102 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 250 $.	2
5539	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $.	2
5540	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5541	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = \left( -74 \right) $.	2
5542	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
5543	Find $ a_{ 101 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = 3 $.	2
5544	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 5 $.	2
5545	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
5546	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 9 $.	2
5547	Find $ a_{ 90 } $ of an arithmetic progression if $ a_1 = -40 ~~ \text{and} ~~ d = 10 $.	2
5548	Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = -40 ~~ \text{and} ~~ d = 90 $.	2
5549	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 15 $.	2
5550	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -6 \right) $.	2