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
5651	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
5652	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -34 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
5653	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 80 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
5654	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	2
5655	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 8 $.	2
5656	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 3 $.	2
5657	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	2
5658	$$ a_1 = 1 ~,~ d = 1 ~,~ a_n = 365 ~,~ n = ? $$	2
5659	Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 8 $.	2
5660	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 4 $.	2
5661	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 86 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
5662	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 56 ~~ \text{and} ~~ d = 10 $.	2
5663	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 2 $.	2
5664	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 64 ~~ \text{and} ~~ d = 5 $.	2
5665	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 64 ~~ \text{and} ~~ d = -5 $.	2
5666	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 12 $.	2
5667	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
5668	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = -7 $.	2
5669	Find $ S_{ 114 } $ ( sum of first $ 114 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
5670	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \frac{ 4 }{ 13 } $.	2
5671	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 13 $.	2
5672	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 100 $.	2
5673	Find $ a_{ 81 } $ of an arithmetic progression if $ a_1 = -28 ~~ \text{and} ~~ d = \left( -62 \right) $.	2
5674	Find $ S_{ 365 } $ ( sum of first $ 365 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $.	2
5675	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -30 \right) $.	2
5676	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
5677	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -33 ~~ \text{and} ~~ d = 3 $.	2
5678	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 72 ~~ \text{and} ~~ d = \left( -24 \right) $.	2
5679	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = -31 ~~ \text{and} ~~ d = 8 $.	2
5680	Find $ a_1 $ (first term of arithmetic progression) if $ d = 2 ~~ \text{and} ~~ a_{ 45 } = 93 $.	2
5681	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 26000 ~~ \text{and} ~~ d = 1250 $.	2
5682	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 395 ~~ \text{and} ~~ d = 45 $.	2
5683	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 8 $.	2
5684	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 1 $.	2
5685	Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 30 $.	2
5686	Find $ S_{ 94 } $ ( sum of first $ 94 $ terms ) of arithmetic progression if $ a_1 = -26 ~~ \text{and} ~~ d = 11 $.	2
5687	Find $ S_{ 91 } $ ( sum of first $ 91 $ terms ) of arithmetic progression if $ a_1 = 45 ~~ \text{and} ~~ d = 1 $.	2
5688	Find $ a_{ 54 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 16 $.	2
5689	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 1000 $.	2
5690	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 10 $.	2
5691	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 10 $.	2
5692	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 10 $.	2
5693	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 1 $.	2
5694	$$ a_1 = \frac{ 1 }{ 60 } ~,~ a_n = 1 ~,~ S_n = 0 ~,~ n = ? $$	2
5695	$$ a_1 = -59 ~,~ a_n = \frac{ 1 }{ 59 } ~,~ S_n = 0 ~,~ n = ? $$	2
5696	$$ a_1 = 1 ~,~ d = 1 ~,~ a_n = 20 ~,~ n = ? $$	2
5697	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ d = 1 $.	2
5698	$$ a_{ 1 } = \frac{ 1 }{ 2 } ~~,~~ S_{ 1 } = \frac{ 1 }{ 2 } ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
5699	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	2
5700	Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	2