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
1151	$$ a_1 = -47 ~,~ d = 7 ~,~ a_n = 72 ~,~ n = ? $$	5
1152	Find $ a_{ 423 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 79 $.	5
1153	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = -2 $.	5
1154	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	5
1155	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 1000 $.	5
1156	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	5
1157	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 1000 $.	5
1158	Find $ a_{ 690 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 0 $.	5
1159	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	5
1160	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 50 $.	5
1161	Find $ a_{ 249 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 50 $.	5
1162	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $.	5
1163	Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ a_{ 5 } = 17 $.	5
1164	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	5
1165	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	5
1166	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	5
1167	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = \left( -3 \right) $.	5
1168	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = -3 $.	5
1169	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	5
1170	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 1 $.	5
1171	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 2 $.	5
1172	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 3 $.	5
1173	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	5
1174	Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ S_{ 5 } = 40 $.	5
1175	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 4 $.	5
1176	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 4 $.	5
1177	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 2 $.	5
1178	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	5
1179	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 13 $.	5
1180	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	5
1181	Find $ a_{ 74 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = \left( -7 \right) $.	5
1182	Find common difference $ d $ of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ a_{ 4 } = 8 $.	5
1183	$$ a_1 = 7 ~,~ d = 7 ~,~ a_n = 98 ~,~ n = ? $$	5
1184	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 7 $.	5
1185	Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ a_{ 15 } = 86 $.	5
1186	Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 5 $.	5
1187	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 130 ~~ \text{and} ~~ d = 2 $.	5
1188	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 2 $.	5
1189	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = \left( -5 \right) $.	5
1190	Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ a_{ 8 } = 22 $.	5
1191	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	5
1192	$$ a_1 = -7 ~~,~~ d = 2 ~~,~~ a_1 = ? ~~,~~ d = ? $$	5
1193	Find $ a_{ 64 } $ of an arithmetic progression if $ a_1 = \frac{ 7 }{ 3 } ~~ \text{and} ~~ d = \frac{ 7 }{ 6 } $.	5
1194	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	5
1195	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = 1 $.	5
1196	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = -\frac{ 1 }{ 2 } $.	5
1197	Find $ a_{ 500 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	5
1198	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	5
1199	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 7 $.	5
1200	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 7 $.	5