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
6051	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 12 $.	2
6052	Find $ a_{ 123 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 6 $.	2
6053	Find $ a_{ 4621 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = 5 $.	2
6054	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 1 $.	2
6055	Find $ a_{ 190 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 13 $.	2
6056	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 190 ~~ \text{and} ~~ d = 13 $.	2
6057	Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	2
6058	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -\frac{ 11 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	2
6059	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	2
6060	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = 1 $.	2
6061	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 4 $.	2
6062	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 4 $.	2
6063	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
6064	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
6065	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
6066	Find $ a_{ 162 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
6067	Find $ a_{ 162 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	2
6068	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 42 $.	2
6069	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 5 $.	2
6070	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
6071	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
6072	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	1
6073	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	1
6074	Find $ a_{ 69 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	1
6075	Find $ a_{ 73 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	1
6076	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 2800 ~~ \text{and} ~~ d = 100 $.	1
6077	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 0 $.	1
6078	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = 300 $.	1
6079	Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = 33 ~~ \text{and} ~~ d = 1 $.	1
6080	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 33 ~~ \text{and} ~~ d = 1 $.	1
6081	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 6 $.	1
6082	Find $ S_{ 400 } $ ( sum of first $ 400 $ terms ) of arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = \frac{ 38 }{ 25 } $.	1
6083	Find $ S_{ 262144 } $ ( sum of first $ 262144 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	1
6084	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 0 $.	1
6085	Find common difference $ d $ of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ a_{ 10 } = 68 $.	1
6086	Find $ a_{ 89 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 15 $.	1
6087	Find $ a_{ 89 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = \left( -15 \right) $.	1
6088	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 5 $.	1
6089	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
6090	Find $ S_{ 67 } $ ( sum of first $ 67 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 5 $.	1
6091	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 5 $.	1
6092	$$ d = 8 ~,~ a_n = 28 ~,~ S_n = 119 ~,~ n = ? $$	1
6093	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \frac{ 683 }{ 50 } $.	1
6094	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 12 $.	1
6095	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -12 \right) $.	1
6096	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = \left( -16 \right) $.	1
6097	Find $ a_{ 55 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -16 \right) $.	1
6098	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 2 $.	1
6099	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	1
6100	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	1