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
1201	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	5
1202	Find $ S_{ 84 } $ ( sum of first $ 84 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	5
1203	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 59 $.	5
1204	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 5 $.	5
1205	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 13 $.	5
1206	Find $ S_{ 101 } $ ( sum of first $ 101 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	5
1207	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 45 ~~ \text{and} ~~ d = 3 $.	5
1208	Find $ a_1 $ (first term of arithmetic progression) if $ d = 6 ~~ \text{and} ~~ a_{ 38 } = -40 $.	5
1209	$$ a_1 = -8 ~,~ d = 5 ~,~ a_n = 322 ~,~ n = ? $$	5
1210	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 18 $.	5
1211	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 23 $.	5
1212	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = \left( -4 \right) $.	5
1213	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	5
1214	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 25 $.	5
1215	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	5
1216	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	5
1217	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 600 ~~ \text{and} ~~ d = 5 $.	5
1218	Find $ a_{ 720 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 20 $.	5
1219	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	5
1220	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 52 ~~ \text{and} ~~ d = 6 $.	5
1221	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = \left( -3 \right) $.	5
1222	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 0 $.	5
1223	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 8 $.	5
1224	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 11 }{ 2 } $.	5
1225	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = 5 $.	5
1226	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	5
1227	$$ a_1 = 9 ~,~ a_n = 17 ~,~ S_n = 9 ~,~ n = ? $$	5
1228	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 50 $.	5
1229	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 6 $.	5
1230	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 4 $.	5
1231	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 11 $.	5
1232	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 11 $.	5
1233	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -1 \right) $.	5
1234	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -1 \right) $.	5
1235	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = \left( -1 \right) $.	5
1236	Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 8 $.	5
1237	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 5 $.	5
1238	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 4 $.	5
1239	Find $ a_{ 65 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 3 $.	5
1240	Find common difference $ d $ of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ a_{ 16 } = 45 $.	5
1241	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 0 $.	5
1242	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 6 $.	5
1243	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 5 $.	5
1244	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	5
1245	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	5
1246	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	5
1247	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 110 ~~ \text{and} ~~ d = 11 $.	5
1248	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = -5 $.	5
1249	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = -5 $.	5
1250	$$ a_1 = 426 ~,~ d = \frac{ 1 }{ 10 } ~,~ S_n = 500 ~,~ n = ? $$	5