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
1101	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = \left( -4 \right) $.	5
1102	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = -16 ~~ \text{and} ~~ d = 3 $.	5
1103	Find $ a_{ 46 } $ of an arithmetic progression if $ a_1 = 156 ~~ \text{and} ~~ d = \left( -3 \right) $.	5
1104	Find $ S_{ 65536 } $ ( sum of first $ 65536 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	5
1105	Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = -40 ~~ \text{and} ~~ d = 5 $.	5
1106	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = \left( -3 \right) $.	5
1107	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -4 \right) $.	5
1108	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -4 \right) $.	5
1109	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -4 \right) $.	5
1110	Find $ a_{ 79 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 91 $.	5
1111	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 3 $.	5
1112	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 3 $.	5
1113	Find $ S_{ 61 } $ ( sum of first $ 61 $ terms ) of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 3 $.	5
1114	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	5
1115	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	5
1116	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 47 }{ 120 } $.	5
1117	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = -\frac{ 7 }{ 10 } ~~ \text{and} ~~ d = \left( -\frac{ 131 }{ 10 } \right) $.	5
1118	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	5
1119	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = -5 $.	5
1120	Find $ S_{ 81 } $ ( sum of first $ 81 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	5
1121	Find $ S_{ 27 } $ ( sum of first $ 27 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	5
1122	Find $ S_{ 55 } $ ( sum of first $ 55 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	5
1123	Find $ S_{ 65 } $ ( sum of first $ 65 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	5
1124	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 7 $.	5
1125	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 7 }{ 20 } ~~ \text{and} ~~ d = \frac{ 7 }{ 20 } $.	5
1126	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	5
1127	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 5 $.	5
1128	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 4 $.	5
1129	Find $ S_{ 365 } $ ( sum of first $ 365 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	5
1130	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = -5 $.	5
1131	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	5
1132	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	5
1133	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	5
1134	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	5
1135	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 7 $.	5
1136	Find $ a_{ 57 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = \left( -3 \right) $.	5
1137	Find $ a_1 $ (first term of arithmetic progression) if $ d = 5 ~~ \text{and} ~~ a_{ 3 } = 28 $.	5
1138	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 0 $.	5
1139	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	5
1140	Find $ S_{ 101 } $ ( sum of first $ 101 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	5
1141	$$ a_1 = -3 ~,~ d = 5 ~,~ a_n = 74 ~,~ n = ? $$	5
1142	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	5
1143	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	5
1144	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	5
1145	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -3 \right) $.	5
1146	Find $ S_{ 99 } $ ( sum of first $ 99 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	5
1147	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 4 $.	5
1148	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	5
1149	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 5 $.	5
1150	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	5