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
3651	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
3652	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
3653	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 8 $.	2
3654	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
3655	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	2
3656	$$ a_1 = 16 ~,~ d = 5 ~,~ S_n = 1633 ~,~ n = ? $$	2
3657	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 8 $.	2
3658	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -37 ~~ \text{and} ~~ d = 0 $.	2
3659	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = -61 ~~ \text{and} ~~ d = 0 $.	2
3660	$$ a_1 = 24 ~,~ d = 55 ~,~ S_n = 794 ~,~ n = ? $$	2
3661	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 1800 ~~ \text{and} ~~ d = 175 $.	2
3662	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 1800 ~~ \text{and} ~~ d = 175 $.	2
3663	$$ a_1 = 48500 ~,~ d = 1200 ~,~ S_n = 32100 ~,~ n = ? $$	2
3664	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
3665	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
3666	Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ S_{ 15 } = 645 $.	2
3667	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 82 ~~ \text{and} ~~ d = 0 $.	2
3668	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 82 ~~ \text{and} ~~ d = 26 $.	2
3669	$$ a_1 = -70 ~,~ d = 840 ~,~ a_n = 21 ~,~ n = ? $$	2
3670	Find $ d $ (common difference of arithmetic progression) if $ a_1 = -70 ~~ \text{and} ~~ S_{ 21 } = 840 $.	2
3671	Find $ d $ (common difference of arithmetic progression) if $ a_1 = -51 ~~ \text{and} ~~ S_{ 22 } = 726 $.	2
3672	$$ a_1 = 610 ~~,~~ d = 6 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
3673	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 2 $.	2
3674	Find $ a_1 $ (first term of arithmetic progression) if $ d = -4 ~~ \text{and} ~~ a_{ 6 } = 0 $.	2
3675	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 8 $.	2
3676	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 9 $.	2
3677	Find $ a_1 $ (first term of arithmetic progression) if $ d = 6 ~~ \text{and} ~~ a_{ 18 } = 72 $.	2
3678	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = -33 ~~ \text{and} ~~ d = 5 $.	2
3679	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
3680	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = -47 ~~ \text{and} ~~ d = 7 $.	2
3681	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = -47 ~~ \text{and} ~~ d = 7 $.	2
3682	Find $ S_{ 500 } $ ( sum of first $ 500 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 25 $.	2
3683	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = -5 $.	2
3684	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 90 ~~ \text{and} ~~ d = 180 $.	2
3685	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 52000 ~~ \text{and} ~~ d = 720 $.	2
3686	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 97 ~~ \text{and} ~~ d = \left( -11 \right) $.	2
3687	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
3688	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -1 \right) $.	2
3689	Find $ a_1 $ (first term of arithmetic progression) if $ d = 6 ~~ \text{and} ~~ S_{ 12 } = 384 $.	2
3690	$$ a_1 = 2 ~,~ a_n = 30 ~,~ S_n = 121 ~,~ n = ? $$	2
3691	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = -7 $.	2
3692	Find common difference $ d $ of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ a_{ 4 } = 52 $.	2
3693	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
3694	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
3695	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $.	2
3696	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -\frac{ 1 }{ 8 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
3697	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 4 $.	2
3698	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
3699	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = -33 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
3700	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 10 $.	2