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
4151	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 3 $.	2
4152	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = -\frac{ 2 }{ 5 } $.	2
4153	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 5 $.	2
4154	Find $ a_{ 69 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	2
4155	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 5 $.	2
4156	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
4157	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	2
4158	Find $ S_{ 116 } $ ( sum of first $ 116 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = -5 $.	2
4159	Find $ S_{ 77 } $ ( sum of first $ 77 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	2
4160	Find $ S_{ 113 } $ ( sum of first $ 113 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = -2 $.	2
4161	Find $ S_{ 142 } $ ( sum of first $ 142 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2
4162	Find $ a_{ 76 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 5 $.	2
4163	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ d = 0 $.	2
4164	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = \frac{ 4 }{ 3 } ~~ \text{and} ~~ d = -\frac{ 1 }{ 3 } $.	2
4165	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 2 $.	2
4166	$$ a_1 = 4 ~,~ d = 9 ~,~ S_n = 58 ~,~ n = ? $$	2
4167	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = -9 $.	2
4168	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = -2 $.	2
4169	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 50 $.	2
4170	Find $ a_{ 76 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 9 $.	2
4171	$$ a_{ 12 } = 100 ~~,~~ S_{ 23 } = 2300 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
4172	Find $ S_{ 23 } $ ( sum of first $ 23 $ terms ) of arithmetic progression if $ a_1 = 2100 ~~ \text{and} ~~ d = 200 $.	2
4173	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	2
4174	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 5 $.	2
4175	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 2 $.	2
4176	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 2 $.	2
4177	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 220 ~~ \text{and} ~~ d = \left( -60 \right) $.	2
4178	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 220 ~~ \text{and} ~~ d = \left( -60 \right) $.	2
4179	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 220 ~~ \text{and} ~~ d = \left( -60 \right) $.	2
4180	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 11 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	2
4181	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 11 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	2
4182	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 11 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	2
4183	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 11 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	2
4184	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 19 }{ 4 } ~~ \text{and} ~~ d = \frac{ 2 }{ 5 } $.	2
4185	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 19 }{ 4 } ~~ \text{and} ~~ d = \frac{ 2 }{ 5 } $.	2
4186	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 19 }{ 4 } ~~ \text{and} ~~ d = \frac{ 2 }{ 5 } $.	2
4187	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 8000 ~~ \text{and} ~~ d = 1 $.	2
4188	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = \frac{ 7 }{ 2 } ~~ \text{and} ~~ d = -\frac{ 1 }{ 2 } $.	2
4189	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
4190	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 8 $.	2
4191	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 16 } ~~ \text{and} ~~ d = 4 $.	2
4192	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -\frac{ 1 }{ 9 } ~~ \text{and} ~~ d = \left( -3 \right) $.	2
4193	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = -2 $.	2
4194	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 160 $.	2
4195	Find $ a_{ 76 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 5 $.	2
4196	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 8 $.	2
4197	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 7 $.	2
4198	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 10 $.	2
4199	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
4200	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2