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
4101	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 6 $.	2
4102	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 3 $.	2
4103	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = \frac{ 73 }{ 4 } ~~ \text{and} ~~ d = \frac{ 9 }{ 2 } $.	2
4104	Find $ a_{ 620 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 7 $.	2
4105	Find $ a_{ 999 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
4106	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
4107	Find $ a_{ 66 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
4108	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 11 }{ 10 } $.	2
4109	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 11 }{ 10 } $.	2
4110	Find $ a_{ 54 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 6 $.	2
4111	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 12 $.	2
4112	Find $ a_{ 92 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 7 $.	2
4113	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 3 $.	2
4114	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 5 $.	2
4115	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 2 $.	2
4116	$$ a_1 = 5 ~,~ d = 2 ~,~ a_n = 103 ~,~ n = ? $$	2
4117	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 305 ~~ \text{and} ~~ d = 55 $.	2
4118	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 305 ~~ \text{and} ~~ d = 55 $.	2
4119	Find $ S_{ 27 } $ ( sum of first $ 27 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 2 $.	2
4120	Find $ a_{ 84 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
4121	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -55 \right) $.	2
4122	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 39 ~~ \text{and} ~~ d = 9 $.	2
4123	Find $ S_{ 61 } $ ( sum of first $ 61 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = -\frac{ 2 }{ 5 } $.	2
4124	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 30 $.	2
4125	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 6 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 3 } \right) $.	2
4126	Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = \left( -20 \right) $.	2
4127	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 9 $.	2
4128	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = -3 $.	2
4129	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 72 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
4130	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 3000 ~~ \text{and} ~~ d = 5 $.	2
4131	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 6000 ~~ \text{and} ~~ d = 100 $.	2
4132	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 100 $.	2
4133	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	2
4134	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 7 $.	2
4135	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = 2 $.	2
4136	Find $ a_{ 51 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
4137	Find $ a_{ 78 } $ of an arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 4 $.	2
4138	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -1 \right) $.	2
4139	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 6 $.	2
4140	$$ a_1 = \frac{ 7 }{ 5 } ~,~ d = \frac{ 3 }{ 20 } ~,~ a_n = 31 ~,~ n = ? $$	2
4141	$$ a_1 = -22 ~,~ d = -9 ~,~ a_n = 1 ~,~ n = ? $$	2
4142	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 122 ~~ \text{and} ~~ d = -3 $.	2
4143	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 92 ~~ \text{and} ~~ d = -5 $.	2
4144	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 233 ~~ \text{and} ~~ d = -20 $.	2
4145	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 0.375 ~~ \text{and} ~~ d = 8 $.	2
4146	$$ a_1 = 2 ~~,~~ d = 3 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
4147	Find common difference $ d $ of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ a_{ 100 } = 307 $.	2
4148	Find $ a_{ 76 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	2
4149	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 8 $.	2
4150	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 3 $.	2