Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 1251 | $$ a_1 = \frac{ 13 }{ 9 } ~~,~~ d = \frac{ 7 }{ 5 } ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 5 |
| 1252 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $. | 5 |
| 1253 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 4 $. | 5 |
| 1254 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $. | 5 |
| 1255 | Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 110 ~~ \text{and} ~~ d = -10 $. | 5 |
| 1256 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 39000 ~~ \text{and} ~~ d = 870 $. | 5 |
| 1257 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -7 \right) $. | 5 |
| 1258 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 0 $. | 5 |
| 1259 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 6 $. | 5 |
| 1260 | Find $ S_{ 129 } $ ( sum of first $ 129 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 3 $. | 5 |
| 1261 | Find $ S_{ 130 } $ ( sum of first $ 130 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 3 $. | 5 |
| 1262 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 500 $. | 5 |
| 1263 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 50 $. | 5 |
| 1264 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 50 $. | 5 |
| 1265 | Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = -5 $. | 5 |
| 1266 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 25 $. | 5 |
| 1267 | Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $. | 5 |
| 1268 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -1 \right) $. | 4 |
| 1269 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ a_{ 15 } = 14 $. | 4 |
| 1270 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 194 ~~ \text{and} ~~ d = \left( -13 \right) $. | 4 |
| 1271 | Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 0 $. | 4 |
| 1272 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -98 ~~ \text{and} ~~ d = \left( -3 \right) $. | 4 |
| 1273 | Find common difference $ d $ of arithmetic progression if $ a_1 = -95 ~~ \text{and} ~~ a_{ 38 } = -200 $. | 4 |
| 1274 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 56 ~~ \text{and} ~~ d = 14 $. | 4 |
| 1275 | $$ a_1 = 56 ~~,~~ d = 14 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 4 |
| 1276 | $$ a_1 = 5 ~,~ a_n = 45 ~,~ S_n = 400 ~,~ n = ? $$ | 4 |
| 1277 | Find $ S_{ 5050 } $ ( sum of first $ 5050 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 1 $. | 4 |
| 1278 | Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1279 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1280 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1281 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1282 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 6 $. | 4 |
| 1283 | Find $ S_{ 5000 } $ ( sum of first $ 5000 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 4 |
| 1284 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1285 | Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1286 | Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1287 | Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1288 | Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1289 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1290 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = \left( -4 \right) $. | 4 |
| 1291 | $$ a_1 = \frac{ 42611 }{ 100 } ~,~ d = \frac{ 1 }{ 10 } ~,~ S_n = 500 ~,~ n = ? $$ | 4 |
| 1292 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 262 ~~ \text{and} ~~ d = 1755 $. | 4 |
| 1293 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 262 ~~ \text{and} ~~ d = 195 $. | 4 |
| 1294 | Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1295 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1296 | Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $. | 4 |
| 1297 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 162 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $. | 4 |
| 1298 | Find $ a_{ 2021 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1299 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1300 | Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 4 |
