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
1051	Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = 10 $.	5
1052	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 0 $.	5
1053	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 7 }{ 2 } ~~ \text{and} ~~ d = \frac{ 2 }{ 5 } $.	5
1054	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 714 ~~ \text{and} ~~ d = 714 $.	5
1055	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 721 ~~ \text{and} ~~ d = 721 $.	5
1056	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 721 ~~ \text{and} ~~ d = 721 $.	5
1057	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = \left( -3 \right) $.	5
1058	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	5
1059	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 3 } \right) $.	5
1060	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = 0 $.	5
1061	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = 0 $.	5
1062	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 4 $.	5
1063	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 25 } ~~ \text{and} ~~ d = \frac{ 4 }{ 25 } $.	5
1064	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = 6 $.	5
1065	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	5
1066	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	5
1067	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 8 } $.	5
1068	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 39 }{ 4 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	5
1069	Find $ a_{ 69 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $.	5
1070	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -1 \right) $.	5
1071	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = -1 $.	5
1072	Find $ a_{ 64 } $ of an arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 9 $.	5
1073	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	5
1074	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 3 $.	5
1075	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1500 ~~ \text{and} ~~ d = -5 $.	5
1076	Find $ a_{ 53 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = \left( -1 \right) $.	5
1077	Find $ S_{ 2500 } $ ( sum of first $ 2500 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 190 $.	5
1078	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	5
1079	Find $ S_{ 65 } $ ( sum of first $ 65 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 8 $.	5
1080	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 16 $.	5
1081	$$ a_1 = 950 ~,~ d = 275 ~,~ a_n = 10575 ~,~ n = ? $$	5
1082	Find $ a_{ 63 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	5
1083	Find $ a_{ 82 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 1 $.	5
1084	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	5
1085	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	5
1086	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \frac{ 3 }{ 10 } $.	5
1087	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 58 $.	5
1088	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 5 $.	5
1089	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -4 \right) $.	5
1090	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	5
1091	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 17 $.	5
1092	$$ a_1 = -9 ~~,~~ d = 11 ~~,~~ a_1 = ? ~~,~~ d = ? $$	5
1093	Find $ S_{ 366 } $ ( sum of first $ 366 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	5
1094	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 4 $.	5
1095	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -6 \right) $.	5
1096	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = -3 $.	5
1097	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \left( -3 \right) $.	5
1098	Find $ S_{ 121 } $ ( sum of first $ 121 $ terms ) of arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = -4 $.	5
1099	$$ a_1 = 1491 ~,~ d = -7 ~,~ S_n = 0 ~,~ n = ? $$	5
1100	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	5