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
4051	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
4052	Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = -29 ~~ \text{and} ~~ d = 2 $.	2
4053	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 6 $.	2
4054	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 4 $.	2
4055	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = 8 $.	2
4056	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 33 ~~ \text{and} ~~ d = 8 $.	2
4057	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = \frac{ 7 }{ 2 } ~~ \text{and} ~~ d = -\frac{ 1 }{ 4 } $.	2
4058	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 17000 ~~ \text{and} ~~ d = 1250 $.	2
4059	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 17000 ~~ \text{and} ~~ d = 1250 $.	2
4060	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 125 ~~ \text{and} ~~ d = 25 $.	2
4061	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = 34458006 ~~ \text{and} ~~ d = 900000 $.	2
4062	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	2
4063	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	2
4064	Find $ a_{ 69 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	2
4065	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = 12 $.	2
4066	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = 10 $.	2
4067	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = 10 $.	2
4068	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = 10 $.	2
4069	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = \left( -20 \right) $.	2
4070	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 349 ~~ \text{and} ~~ d = 8 $.	2
4071	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 4 $.	2
4072	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 1 $.	2
4073	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	2
4074	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 6 $.	2
4075	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 110 ~~ \text{and} ~~ d = 35 $.	2
4076	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 178 ~~ \text{and} ~~ d = -4 $.	2
4077	Find $ S_{ 149 } $ ( sum of first $ 149 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 5 $.	2
4078	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -9 \right) $.	2
4079	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 98 ~~ \text{and} ~~ d = 9 $.	2
4080	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = -\frac{ 1 }{ 2 } $.	2
4081	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = -\frac{ 7 }{ 2 } $.	2
4082	Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 3 $.	2
4083	Find $ S_{ 120 } $ ( sum of first $ 120 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 2 $.	2
4084	Find $ S_{ 201 } $ ( sum of first $ 201 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	2
4085	Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 8 $.	2
4086	Find $ a_{ 77 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 6 $.	2
4087	Find $ S_{ 67 } $ ( sum of first $ 67 $ terms ) of arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 30 $.	2
4088	Find $ S_{ 112 } $ ( sum of first $ 112 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4089	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	2
4090	Find $ S_{ 400 } $ ( sum of first $ 400 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 11 $.	2
4091	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 2 $.	2
4092	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = -8 $.	2
4093	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = \frac{ 763 }{ 10 } ~~ \text{and} ~~ d = -\frac{ 4 }{ 5 } $.	2
4094	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = -6 $.	2
4095	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 250 ~~ \text{and} ~~ d = \left( -15 \right) $.	2
4096	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 7 $.	2
4097	Find common difference $ d $ of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ a_{ 9 } = 19 $.	2
4098	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 7 $.	2
4099	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 3 $.	2
4100	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 7 $.	2