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
6101	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 8 $.	1
6102	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 9 $.	1
6103	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 9 $.	1
6104	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 1 $.	1
6105	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 9 $.	1
6106	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 10 $.	1
6107	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 10 $.	1
6108	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 10 $.	1
6109	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 9 $.	1
6110	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 10 $.	1
6111	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 9 $.	1
6112	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
6113	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	1
6114	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	1
6115	Find $ a_{ 78 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = \frac{ 15 }{ 2 } $.	1
6116	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = 6 $.	1
6117	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 0 $.	1
6118	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 5 $.	1
6119	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 2 $.	1
6120	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 2 $.	1
6121	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 50 $.	1
6122	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	1
6123	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = \frac{ 17 }{ 10 } ~~ \text{and} ~~ d = \frac{ 1 }{ 5 } $.	1
6124	Find $ a_{ 999 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	1
6125	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 6 $.	1
6126	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
6127	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = 0 $.	1
6128	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 0 $.	1
6129	Find $ a_{ 59 } $ of an arithmetic progression if $ a_1 = \frac{ 13 }{ 2 } ~~ \text{and} ~~ d = \frac{ 11 }{ 10 } $.	1
6130	Find $ a_{ 69 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	1
6131	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = 100 $.	1
6132	$$ a_1 = 13 ~,~ d = -2 ~,~ a_n = -13 ~,~ n = ? $$	1
6133	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -10 \right) $.	1
6134	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -36 ~~ \text{and} ~~ d = 2 $.	1
6135	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ d = \frac{ 1 }{ 20 } $.	1
6136	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 3 $.	1
6137	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 87 ~~ \text{and} ~~ d = 0 $.	1
6138	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 87 ~~ \text{and} ~~ d = 11 $.	1
6139	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 87 ~~ \text{and} ~~ d = \left( -11 \right) $.	1
6140	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 87 ~~ \text{and} ~~ d = -11 $.	1
6141	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = \frac{ 4 }{ 5 } ~~ \text{and} ~~ d = \left( -2 \right) $.	1
6142	Find $ S_{ 43 } $ ( sum of first $ 43 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 2 $.	1
6143	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \left( -7 \right) $.	1
6144	Find $ S_{ 75 } $ ( sum of first $ 75 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	1
6145	$$ a_{ 4 } = 21 ~~,~~ S_{ 6 } = 32 ~~,~~ a_1 = ? ~~,~~ d = ? $$	1
6146	Find $ S_{ 398 } $ ( sum of first $ 398 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	1
6147	Find $ S_{ 79 } $ ( sum of first $ 79 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	1
6148	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 10 $.	1
6149	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	1
6150	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = -1 $.	1