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
5151	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 66 ~~ \text{and} ~~ d = 49 $.	2
5152	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 87 ~~ \text{and} ~~ d = 5 $.	2
5153	Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 87 ~~ \text{and} ~~ d = 5 $.	2
5154	Find $ S_{ 46 } $ ( sum of first $ 46 $ terms ) of arithmetic progression if $ a_1 = 55 ~~ \text{and} ~~ d = 98 $.	2
5155	Find $ S_{ 77 } $ ( sum of first $ 77 $ terms ) of arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 83 $.	2
5156	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 83 $.	2
5157	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	2
5158	Find $ S_{ 120 } $ ( sum of first $ 120 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	2
5159	Find $ S_{ 120 } $ ( sum of first $ 120 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 50 $.	2
5160	Find $ S_{ 120 } $ ( sum of first $ 120 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 25 $.	2
5161	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	2
5162	Find $ a_{ 95 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = \left( -9 \right) $.	2
5163	Find common difference $ d $ of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ a_{ 7 } = 35 $.	2
5164	Find common difference $ d $ of arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ a_{ 10 } = 48 $.	2
5165	$$ a_1 = -8 ~~,~~ d = 5 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
5166	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 64 ~~ \text{and} ~~ d = 61 $.	2
5167	Find $ S_{ 53 } $ ( sum of first $ 53 $ terms ) of arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 16 $.	2
5168	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 7 $.	2
5169	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	2
5170	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $.	2
5171	Find $ a_{ 53 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 16 $.	2
5172	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $.	2
5173	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 1 $.	2
5174	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
5175	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 1 $.	2
5176	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
5177	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 9 $.	2
5178	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 9 $.	2
5179	Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 8 $.	2
5180	Find $ S_{ 42 } $ ( sum of first $ 42 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 58 $.	2
5181	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = 56 $.	2
5182	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 61 ~~ \text{and} ~~ d = 15 $.	2
5183	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 61 ~~ \text{and} ~~ d = 15 $.	2
5184	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	2
5185	Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2
5186	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2
5187	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	2
5188	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 5 $.	2
5189	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 5 $.	2
5190	Find $ a_{ 300 } $ of an arithmetic progression if $ a_1 = 219 ~~ \text{and} ~~ d = 7 $.	2
5191	Find $ a_{ 275 } $ of an arithmetic progression if $ a_1 = 219 ~~ \text{and} ~~ d = 7 $.	2
5192	Find $ a_{ 258 } $ of an arithmetic progression if $ a_1 = 219 ~~ \text{and} ~~ d = 7 $.	2
5193	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 2 $.	2
5194	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 0 $.	2
5195	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = -33 ~~ \text{and} ~~ d = 4 $.	2
5196	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
5197	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = -4 $.	2
5198	Find $ S_{ 127 } $ ( sum of first $ 127 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	2
5199	Find $ S_{ 126 } $ ( sum of first $ 126 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	2
5200	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 5 $.	2