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
5801	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 120 ~~ \text{and} ~~ d = -10 $.	2
5802	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 10 $.	2
5803	$$ a_1 = 1 ~,~ d = 2 ~,~ S_n = 0 ~,~ n = ? $$	2
5804	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5805	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 8 } \right) $.	2
5806	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	2
5807	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	2
5808	Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	2
5809	Find $ S_{ 204 } $ ( sum of first $ 204 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	2
5810	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 5 $.	2
5811	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 10 $.	2
5812	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
5813	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 5 $.	2
5814	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 10 $.	2
5815	Find $ a_1 $ (first term of arithmetic progression) if $ d = -3 ~~ \text{and} ~~ a_{ 31 } = -108 $.	2
5816	$$ d = 8 ~,~ a_n = 28 ~,~ S_n = 11 ~,~ n = ? $$	2
5817	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
5818	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $.	2
5819	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 2 $.	2
5820	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 8 $.	2
5821	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 9 $.	2
5822	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 9 $.	2
5823	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 5 $.	2
5824	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 76 ~~ \text{and} ~~ d = \left( -\frac{ 11 }{ 2 } \right) $.	2
5825	Find $ S_{ 27 } $ ( sum of first $ 27 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 50 } ~~ \text{and} ~~ d = \frac{ 1 }{ 25 } $.	2
5826	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 76 ~~ \text{and} ~~ d = 25 $.	2
5827	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	2
5828	Find common difference $ d $ of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ a_{ 2 } = 11 $.	2
5829	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	2
5830	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 8 $.	2
5831	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 7 $.	2
5832	Find $ a_{ 58 } $ of an arithmetic progression if $ a_1 = -28 ~~ \text{and} ~~ d = \left( -15 \right) $.	2
5833	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 3 $.	2
5834	Find $ a_{ 999 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
5835	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 13200 ~~ \text{and} ~~ d = \frac{ 3 }{ 100 } $.	2
5836	Find $ a_{ 302 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	2
5837	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 50 $.	2
5838	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 50 $.	2
5839	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
5840	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 2 $.	2
5841	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	2
5842	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
5843	Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 7 $.	2
5844	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
5845	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = 100 $.	2
5846	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
5847	$$ a_1 = 6 ~,~ d = 2 ~,~ a_n = 1536 ~,~ n = ? $$	2
5848	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 2 $.	2
5849	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = -19 ~~ \text{and} ~~ d = \left( -30 \right) $.	2
5850	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 11 $.	2