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
5001	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 3 $.	2
5002	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 2 $.	2
5003	Find $ S_{ 1 } $ ( sum of first $ 1 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 50 $.	2
5004	Find $ a_{ 64 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5005	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 30 $.	2
5006	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 6 $.	2
5007	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	2
5008	Find $ S_{ 2356 } $ ( sum of first $ 2356 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	2
5009	Find $ a_{ 2021 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	2
5010	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 17 }{ 3 } ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $.	2
5011	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 11 }{ 10 } $.	2
5012	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 4 $.	2
5013	Find $ S_{ 180 } $ ( sum of first $ 180 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 0 $.	2
5014	Find $ S_{ 180 } $ ( sum of first $ 180 $ terms ) of arithmetic progression if $ a_1 = 20000 ~~ \text{and} ~~ d = 0 $.	2
5015	Find $ a_{ 180 } $ of an arithmetic progression if $ a_1 = 20000 ~~ \text{and} ~~ d = 200 $.	2
5016	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
5017	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = -13 $.	2
5018	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
5019	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 0 $.	2
5020	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -\frac{ 146 }{ 3 } ~~ \text{and} ~~ d = \frac{ 13 }{ 3 } $.	2
5021	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = -39 ~~ \text{and} ~~ d = \left( -30 \right) $.	2
5022	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -48 ~~ \text{and} ~~ d = \frac{ 11 }{ 3 } $.	2
5023	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 39 ~~ \text{and} ~~ d = \left( -30 \right) $.	2
5024	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -\frac{ 142 }{ 3 } ~~ \text{and} ~~ d = \frac{ 11 }{ 3 } $.	2
5025	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -\frac{ 142 }{ 3 } ~~ \text{and} ~~ d = \frac{ 11 }{ 4 } $.	2
5026	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = \left( -\frac{ 5 }{ 4 } \right) $.	2
5027	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
5028	Find $ S_{ 99 } $ ( sum of first $ 99 $ terms ) of arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = 50 $.	2
5029	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = 50 $.	2
5030	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 0 $.	2
5031	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 8 $.	2
5032	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = -7 $.	2
5033	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 8 $.	2
5034	Find $ a_{ 59 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	2
5035	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	2
5036	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = 1 $.	2
5037	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5038	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = -2 $.	2
5039	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 30 $.	2
5040	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 30 $.	2
5041	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 6 $.	2
5042	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 5 $.	2
5043	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 8 }{ 3 } ~~ \text{and} ~~ d = \frac{ 3 }{ 5 } $.	2
5044	Find $ a_{ 336 } $ of an arithmetic progression if $ a_1 = 20000 ~~ \text{and} ~~ d = 200 $.	2
5045	Find $ a_{ 336 } $ of an arithmetic progression if $ a_1 = 20000 ~~ \text{and} ~~ d = 653 $.	2
5046	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5047	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = -23 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
5048	Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	2
5049	Find $ a_{ 300 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	2
5050	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	2