Arithmetic sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Arithmetic sequences.

Select category

ID	Problem	Count
4951	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2
4952	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 8 $.	2
4953	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 0 $.	2
4954	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 6 $.	2
4955	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 1 $.	2
4956	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 7 $.	2
4957	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	2
4958	Find $ a_{ 63 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4959	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 9 $.	2
4960	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 19900 ~~ \text{and} ~~ d = 1300 $.	2
4961	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 19900 ~~ \text{and} ~~ d = 1900 $.	2
4962	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 10 $.	2
4963	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 10 $.	2
4964	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 10 $.	2
4965	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 10 $.	2
4966	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 11 $.	2
4967	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 16700 ~~ \text{and} ~~ d = 1300 $.	2
4968	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	2
4969	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 6 $.	2
4970	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 12 $.	2
4971	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 12 $.	2
4972	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \frac{ 259 }{ 5 } $.	2
4973	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 8 $.	2
4974	Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
4975	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 6 $.	2
4976	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 95 ~~ \text{and} ~~ d = \frac{ 11 }{ 2 } $.	2
4977	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 4 $.	2
4978	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 4 } ~~ \text{and} ~~ d = \frac{ 5 }{ 4 } $.	2
4979	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 0 $.	2
4980	Find $ a_1 $ (first term of arithmetic progression) if $ d = 7 ~~ \text{and} ~~ S_{ 19 } = 1938 $.	2
4981	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = 0 $.	2
4982	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = 0 $.	2
4983	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = 2 $.	2
4984	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = -2 $.	2
4985	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = \left( -15 \right) $.	2
4986	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = -16 $.	2
4987	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = -11 $.	2
4988	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 92 ~~ \text{and} ~~ d = -10 $.	2
4989	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 137 ~~ \text{and} ~~ d = -11 $.	2
4990	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 137 ~~ \text{and} ~~ d = \left( -11 \right) $.	2
4991	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 115 ~~ \text{and} ~~ d = -8 $.	2
4992	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 115 ~~ \text{and} ~~ d = -8 $.	2
4993	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 115 ~~ \text{and} ~~ d = -8 $.	2
4994	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 115 ~~ \text{and} ~~ d = -8 $.	2
4995	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 115 ~~ \text{and} ~~ d = -8 $.	2
4996	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 129 ~~ \text{and} ~~ d = -8 $.	2
4997	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 4 $.	2
4998	Find $ S_{ 94 } $ ( sum of first $ 94 $ terms ) of arithmetic progression if $ a_1 = 94 ~~ \text{and} ~~ d = 1 $.	2
4999	Find $ d $ (common difference of arithmetic progression) if $ a_1 = \frac{ 5 }{ 3 } ~~ \text{and} ~~ S_{ 26 } = \frac{ 91 }{ 3 } $.	2
5000	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2