Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 1301 | Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 4100 ~~ \text{and} ~~ d = 100 $. | 4 |
| 1302 | Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = -1 $. | 4 |
| 1303 | Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = \frac{ 4 }{ 5 } ~~ \text{and} ~~ d = \left( -2 \right) $. | 4 |
| 1304 | Find $ S_{ 196 } $ ( sum of first $ 196 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 4 |
| 1305 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 39000 ~~ \text{and} ~~ d = 870 $. | 4 |
| 1306 | $$ a_1 = 1 ~,~ d = 1 ~,~ a_n = 52 ~,~ n = ? $$ | 4 |
| 1307 | Find $ S_{ 82 } $ ( sum of first $ 82 $ terms ) of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 16 $. | 4 |
| 1308 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 6 $. | 4 |
| 1309 | Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1310 | Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 32 $. | 4 |
| 1311 | Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 32 $. | 4 |
| 1312 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $. | 4 |
| 1313 | Find $ S_{ 2000 } $ ( sum of first $ 2000 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 4 |
| 1314 | Find $ S_{ 75 } $ ( sum of first $ 75 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $. | 4 |
| 1315 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 4 |
| 1316 | Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 25 $. | 4 |
| 1317 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 7 $. | 4 |
| 1318 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 6 $. | 4 |
| 1319 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 6 $. | 4 |
| 1320 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = 7 $. | 4 |
| 1321 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -3 \right) $. | 4 |
| 1322 | $$ a_1 = 5000 ~,~ a_n = 5000 ~,~ S_n = 100000 ~,~ n = ? $$ | 4 |
| 1323 | Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 6 $. | 4 |
| 1324 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 30 $. | 4 |
| 1325 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $. | 4 |
| 1326 | $$ a_1 = 8 ~,~ d = 4 ~,~ a_n = 200 ~,~ n = ? $$ | 4 |
| 1327 | $$ a_1 = 1 ~,~ d = 1 ~,~ a_n = 6 ~,~ n = ? $$ | 4 |
| 1328 | Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $. | 4 |
| 1329 | Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1330 | $$ a_1 = 5 ~~,~~ d = 10 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 4 |
| 1331 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $. | 4 |
| 1332 | Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 12 $. | 4 |
| 1333 | Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -12 \right) $. | 4 |
| 1334 | Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -14 \right) $. | 4 |
| 1335 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 13 $. | 4 |
| 1336 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1337 | $$ a_1 = -\frac{ 36 }{ 5 } ~,~ d = \frac{ 18 }{ 5 } ~,~ a_n = \frac{ 36 }{ 5 } ~,~ n = ? $$ | 4 |
| 1338 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1339 | Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 9 $. | 4 |
| 1340 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1341 | Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1342 | Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 3520 ~~ \text{and} ~~ d = 20 $. | 4 |
| 1343 | Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1344 | Find $ S_{ 226 } $ ( sum of first $ 226 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $. | 4 |
| 1345 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 11 ~~ \text{and} ~~ a_{ 27 } = 263 $. | 4 |
| 1346 | $$ a_1 = -23 ~,~ d = 11 ~,~ a_n = 516 ~,~ n = ? $$ | 4 |
| 1347 | Find $ d $ (common difference of arithmetic progression) if $ a_1 = -7 ~~ \text{and} ~~ S_{ 20 } = 620 $. | 4 |
| 1348 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -2 \right) $. | 4 |
| 1349 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = 0 $. | 4 |
| 1350 | Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = 180 ~~ \text{and} ~~ d = 60 $. | 4 |
