Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 7451 | $$ a_1 = 15 ~,~ d = -1 ~,~ a_n = 1 ~,~ n = ? $$ | 1 |
| 7452 | Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 49 }{ 10 } ~~ \text{and} ~~ d = \frac{ 4 }{ 5 } $. | 1 |
| 7453 | $$ a_1 = \frac{ 35 }{ 4 } ~,~ d = \frac{ 19 }{ 20 } ~,~ S_n = \frac{ 85 }{ 2 } ~,~ n = ? $$ | 1 |
| 7454 | Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 1 |
| 7455 | Find $ S_{ 10000 } $ ( sum of first $ 10000 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 5 $. | 1 |
| 7456 | Find $ a_{ 81 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $. | 1 |
| 7457 | Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $. | 1 |
| 7458 | Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $. | 1 |
| 7459 | Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = -5 $. | 1 |
| 7460 | $$ a_1 = 6 ~,~ d = 4 ~,~ S_n = 126 ~,~ n = ? $$ | 1 |
| 7461 | Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 6 $. | 1 |
| 7462 | $$ a_1 = 11 ~,~ d = 6 ~,~ S_n = 365 ~,~ n = ? $$ | 1 |
| 7463 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 125000 ~~ \text{and} ~~ d = 5000 $. | 1 |
| 7464 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 125000 ~~ \text{and} ~~ d = 5000 $. | 1 |
| 7465 | $$ a_1 = 306 ~,~ d = 6 ~,~ a_n = 498 ~,~ n = ? $$ | 1 |
| 7466 | Find $ a_1 $ (first term of arithmetic progression) if $ d = -3 ~~ \text{and} ~~ a_{ 15 } = -35 $. | 1 |
| 7467 | Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 2 $. | 1 |
| 7468 | Find $ a_1 $ (first term of arithmetic progression) if $ d = -\frac{ 3 }{ 2 } ~~ \text{and} ~~ a_{ 21 } = -25 $. | 1 |
| 7469 | Find $ a_{ 68 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 8 $. | 1 |
| 7470 | Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 110 $. | 1 |
| 7471 | Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7472 | Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7473 | Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7474 | Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7475 | Find $ S_{ 34 } $ ( sum of first $ 34 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7476 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -7 \right) $. | 1 |
| 7477 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -6 \right) $. | 1 |
| 7478 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -8 \right) $. | 1 |
| 7479 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = -8 $. | 1 |
| 7480 | Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 78 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7481 | Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 79 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7482 | Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 1 |
| 7483 | Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 6 $. | 1 |
| 7484 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 8247 }{ 100 } ~~ \text{and} ~~ d = \frac{ 8247 }{ 100 } $. | 1 |
| 7485 | $$ a_1 = -6 ~~,~~ d = -9 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 7486 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \frac{ 31 }{ 68 } $. | 1 |
| 7487 | $$ a_1 = -15 ~,~ d = 7 ~,~ S_n = 801 ~,~ n = ? $$ | 1 |
| 7488 | Find common difference $ d $ of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ a_{ 100 } = 205 $. | 1 |
| 7489 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 2 $. | 1 |
| 7490 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = \frac{ 11 }{ 12 } ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $. | 1 |
| 7491 | Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7492 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = 6 $. | 1 |
| 7493 | Find $ S_{ 81 } $ ( sum of first $ 81 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7494 | Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 33 ~~ \text{and} ~~ d = 2 $. | 1 |
| 7495 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $. | 1 |
| 7496 | Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $. | 1 |
| 7497 | Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 7498 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = -3 $. | 1 |
| 7499 | Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7500 | Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $. | 1 |
