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
8851	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = \left( -7 \right) $.	1
8852	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = \left( -7 \right) $.	1
8853	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	1
8854	Find $ S_{ 56 } $ ( sum of first $ 56 $ terms ) of arithmetic progression if $ a_1 = 508 ~~ \text{and} ~~ d = -9 $.	1
8855	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
8856	Find $ S_{ 49 } $ ( sum of first $ 49 $ terms ) of arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 0 $.	1
8857	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 4 $.	1
8858	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = -18 ~~ \text{and} ~~ d = 8 $.	1
8859	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = \left( -200 \right) $.	1
8860	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	1
8861	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = -30 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
8862	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = 10 $.	1
8863	Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -9 \right) $.	1
8864	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = -38 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
8865	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 4 $.	1
8866	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
8867	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = -\frac{ 9 }{ 2 } ~~ \text{and} ~~ d = 0 $.	1
8868	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $.	1
8869	Find $ S_{ 300 } $ ( sum of first $ 300 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $.	1
8870	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
8871	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 6 $.	1
8872	$$ a_{ 2 } = 7 ~~,~~ S_{ 4 } = 12 ~~,~~ a_1 = ? ~~,~~ d = ? $$	1
8873	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
8874	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -1 \right) $.	1
8875	$$ a_1 = 15 ~,~ d = -8 ~,~ S_n = -89 ~,~ n = ? $$	1
8876	Find $ a_{ 56 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 2 $.	1
8877	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	1
8878	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 16 }{ 5 } $.	1
8879	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 2 $.	1
8880	Find $ a_{ 84 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
8881	Find $ a_{ 84 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
8882	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 4 $.	1
8883	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 999 $.	1
8884	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = -113 ~~ \text{and} ~~ d = 0 $.	1
8885	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 11 $.	1
8886	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 9 $.	1
8887	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 58 $.	1
8888	Find $ a_{ 82 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 47 $.	1
8889	Find $ a_{ 46 } $ of an arithmetic progression if $ a_1 = 55 ~~ \text{and} ~~ d = 98 $.	1
8890	Find $ a_{ 77 } $ of an arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 83 $.	1
8891	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 83 $.	1
8892	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 145 ~~ \text{and} ~~ d = 5 $.	1
8893	Find $ a_{ 120 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	1
8894	Find $ a_{ 120 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 25 $.	1
8895	Find $ S_{ 300 } $ ( sum of first $ 300 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1000 $.	1
8896	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 2 $.	1
8897	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	1
8898	Find $ a_1 $ (first term of arithmetic progression) if $ d = -5 ~~ \text{and} ~~ a_{ 36 } = 46 $.	1
8899	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 5 $.	1
8900	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 96 ~~ \text{and} ~~ d = 94 $.	1