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
3601	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 6 $.	2
3602	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 3 $.	2
3603	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	2
3604	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
3605	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 8 $.	2
3606	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	2
3607	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 33 ~~ \text{and} ~~ d = 8 $.	2
3608	Find $ S_{ 101 } $ ( sum of first $ 101 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 4 $.	2
3609	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 6 $.	2
3610	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = -53 ~~ \text{and} ~~ d = 13 $.	2
3611	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = -6 $.	2
3612	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	2
3613	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 4 $.	2
3614	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = -12 $.	2
3615	$$ a_1 = 2 ~,~ d = -\frac{ 1 }{ 2 } ~,~ a_n = 15 ~,~ n = ? $$	2
3616	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	2
3617	$$ a_1 = 2 ~,~ d = -\frac{ 1 }{ 2 } ~,~ a_n = 15 ~,~ n = ? $$	2
3618	Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	2
3619	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 5 $.	2
3620	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 1 $.	2
3621	Find $ a_{ 966 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
3622	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 4 } ~~ \text{and} ~~ d = 1 $.	2
3623	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 55 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
3624	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 5 }{ 4 } ~~ \text{and} ~~ d = 1 $.	2
3625	Find $ S_{ 80 } $ ( sum of first $ 80 $ terms ) of arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = \frac{ 7 }{ 2 } $.	2
3626	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 3 $.	2
3627	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = \frac{ 7 }{ 2 } $.	2
3628	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 5 $.	2
3629	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	2
3630	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -19 ~~ \text{and} ~~ d = 11 $.	2
3631	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	2
3632	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	2
3633	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = \left( -\frac{ 3 }{ 2 } \right) $.	2
3634	$$ a_1 = 15 ~,~ d = -3 ~,~ a_n = -3 ~,~ n = ? $$	2
3635	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 6 $.	2
3636	Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 4 $.	2
3637	Find $ S_{ 42 } $ ( sum of first $ 42 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	2
3638	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 18 $.	2
3639	$$ a_1 = 3 ~,~ d = 5 ~,~ S_n = 2000 ~,~ n = ? $$	2
3640	Find common difference $ d $ of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ a_{ 7 } = 12 $.	2
3641	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
3642	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
3643	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 25 $.	2
3644	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 0 $.	2
3645	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = \frac{ 23 }{ 12 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
3646	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = \frac{ 23 }{ 12 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
3647	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = \frac{ 23 }{ 12 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
3648	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = \frac{ 23 }{ 12 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
3649	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = \left( -1 \right) $.	2
3650	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -4 \right) $.	2