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
5951	Find $ S_{ 120 } $ ( sum of first $ 120 $ terms ) of arithmetic progression if $ a_1 = 2405 ~~ \text{and} ~~ d = 5 $.	2
5952	Find $ S_{ 72 } $ ( sum of first $ 72 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
5953	Find $ a_1 $ (first term of arithmetic progression) if $ d = -9 ~~ \text{and} ~~ a_{ 15 } = -10 $.	2
5954	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 116 ~~ \text{and} ~~ d = \left( -9 \right) $.	2
5955	Find common difference $ d $ of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ a_{ 2 } = -14 $.	2
5956	Find common difference $ d $ of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ a_{ 3 } = -22 $.	2
5957	Find $ a_{ 100000 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 350 $.	2
5958	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 5 $.	2
5959	$$ a_{ 24 } = -506 ~~,~~ S_{ 29 } = -9454 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
5960	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = -46 ~~ \text{and} ~~ d = -20 $.	2
5961	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = -34 ~~ \text{and} ~~ d = 30 $.	2
5962	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	2
5963	$$ a_{ 83 } = 680 ~~,~~ S_{ 4 } = 48 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
5964	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = -\frac{ 72 }{ 161 } ~~ \text{and} ~~ d = \frac{ 1336 }{ 161 } $.	2
5965	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 3 $.	2
5966	$$ a_1 = 365 ~,~ d = -1 ~,~ a_n = 31 ~,~ n = ? $$	2
5967	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 365 ~~ \text{and} ~~ d = -1 $.	2
5968	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 120 ~~ \text{and} ~~ d = \left( -1 \right) $.	2
5969	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
5970	$$ a_1 = 8 ~,~ d = -5 ~,~ a_n = -102 ~,~ n = ? $$	2
5971	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ d = 1 $.	2
5972	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
5973	Find $ a_{ 130 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
5974	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
5975	$$ a_1 = 3 ~,~ d = 3 ~,~ a_n = 165 ~,~ n = ? $$	2
5976	Find $ S_{ 55 } $ ( sum of first $ 55 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
5977	Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	2
5978	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 47 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5979	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 3 $.	2
5980	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 101 ~~ \text{and} ~~ d = 9 $.	2
5981	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = \left( -\frac{ 4 }{ 5 } \right) $.	2
5982	$$ a_1 = 28 ~,~ a_n = 3 ~,~ S_n = 73 ~,~ n = ? $$	2
5983	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 25 $.	2
5984	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	2
5985	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	2
5986	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $.	2
5987	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 2 $.	2
5988	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	2
5989	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 5 $.	2
5990	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 4 $.	2
5991	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 5 $.	2
5992	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	2
5993	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	2
5994	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
5995	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 8 $.	2
5996	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	2
5997	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	2
5998	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	2
5999	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	2
6000	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 5 $.	2