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
4901	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 91 ~~ \text{and} ~~ d = 2 $.	2
4902	$$ a_1 = 91 ~,~ d = 2 ~,~ a_n = 22000 ~,~ n = ? $$	2
4903	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 91 ~~ \text{and} ~~ d = 2 $.	2
4904	Find $ a_{ 168 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4905	Find $ S_{ 168 } $ ( sum of first $ 168 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4906	Find $ S_{ 336 } $ ( sum of first $ 336 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4907	Find $ S_{ 504 } $ ( sum of first $ 504 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4908	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $.	2
4909	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
4910	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
4911	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 43 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
4912	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 7 $.	2
4913	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 10 $.	2
4914	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $.	2
4915	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 5 $.	2
4916	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -31 ~~ \text{and} ~~ d = \left( -39 \right) $.	2
4917	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 1700 ~~ \text{and} ~~ d = 60 $.	2
4918	Find $ a_{ 90 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4919	Find $ S_{ 999 } $ ( sum of first $ 999 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
4920	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 1 $.	2
4921	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 4 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
4922	$$ a_1 = -11 ~,~ a_n = -71 ~,~ S_n = -451 ~,~ n = ? $$	2
4923	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 7 }{ 4 } $.	2
4924	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 7 $.	2
4925	Find $ a_{ 57 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = \left( -15 \right) $.	2
4926	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 0 $.	2
4927	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
4928	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $.	2
4929	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $.	2
4930	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 7 $.	2
4931	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
4932	$$ a_{ 5 } = 21 ~~,~~ S_{ 15 } = 495 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
4933	Find $ a_{ 73 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	2
4934	Find $ a_{ 55 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 9 $.	2
4935	Find $ S_{ 29 } $ ( sum of first $ 29 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = -3 $.	2
4936	$$ a_1 = 13 ~,~ d = 8 ~,~ a_n = 632 ~,~ n = ? $$	2
4937	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	2
4938	Find $ S_{ 99 } $ ( sum of first $ 99 $ terms ) of arithmetic progression if $ a_1 = 296 ~~ \text{and} ~~ d = -3 $.	2
4939	Find $ a_1 $ (first term of arithmetic progression) if $ d = 100 ~~ \text{and} ~~ a_{ 35 } = 3369 $.	2
4940	Find $ a_1 $ (first term of arithmetic progression) if $ d = 100 ~~ \text{and} ~~ a_{ 38 } = 3732 $.	2
4941	Find $ a_1 $ (first term of arithmetic progression) if $ d = 100 ~~ \text{and} ~~ a_{ 12 } = 1069 $.	2
4942	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = -31 ~~ \text{and} ~~ d = 100 $.	2
4943	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
4944	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 0 $.	2
4945	Find $ a_{ 43 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 4 $.	2
4946	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
4947	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	2
4948	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
4949	Find $ S_{ 54 } $ ( sum of first $ 54 $ terms ) of arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = -4 $.	2
4950	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2