Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 501 | Find $ a_{ 231 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $. | 6 |
| 502 | Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $. | 6 |
| 503 | $$ a_{ 8 } = 7 ~~,~~ S_{ 8 } = 64 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 6 |
| 504 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 7 $. | 6 |
| 505 | Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -5 \right) $. | 6 |
| 506 | Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 27 ~~ \text{and} ~~ d = 5 $. | 6 |
| 507 | Find $ a_{ 59 } $ of an arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 8 $. | 6 |
| 508 | Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = \left( -11 \right) $. | 6 |
| 509 | $$ a_1 = -5 ~,~ d = 2 ~,~ a_n = 73 ~,~ n = ? $$ | 6 |
| 510 | Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = 50 $. | 6 |
| 511 | Find $ S_{ 34 } $ ( sum of first $ 34 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $. | 6 |
| 512 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 4 $. | 6 |
| 513 | Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 72000 ~~ \text{and} ~~ d = 18000 $. | 6 |
| 514 | Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = \frac{ 25 }{ 2 } ~~ \text{and} ~~ d = \frac{ 6 }{ 5 } $. | 6 |
| 515 | $$ a_1 = 2 ~,~ d = 2 ~,~ a_n = 20 ~,~ n = ? $$ | 6 |
| 516 | Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \left( -3 \right) $. | 6 |
| 517 | Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = 160 ~~ \text{and} ~~ d = 80 $. | 6 |
| 518 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $. | 6 |
| 519 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 2 $. | 6 |
| 520 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $. | 6 |
| 521 | Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $. | 6 |
| 522 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 330 ~~ \text{and} ~~ d = \left( -90 \right) $. | 6 |
| 523 | $$ a_1 = \frac{ 1 }{ 10 } ~,~ d = \frac{ 1 }{ 10 } ~,~ S_n = 1250 ~,~ n = ? $$ | 6 |
| 524 | Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = \frac{ 4 }{ 5 } ~~ \text{and} ~~ d = 10 $. | 6 |
| 525 | Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $. | 6 |
| 526 | Find $ S_{ 93 } $ ( sum of first $ 93 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = 1 $. | 6 |
| 527 | Find $ a_{ 93 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 7 $. | 6 |
| 528 | Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = -40 ~~ \text{and} ~~ d = 15 $. | 6 |
| 529 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $. | 6 |
| 530 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $. | 6 |
| 531 | Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 11 $. | 6 |
| 532 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $. | 6 |
| 533 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 6 |
| 534 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $. | 6 |
| 535 | Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $. | 6 |
| 536 | Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = \frac{ 11 }{ 10 } ~~ \text{and} ~~ d = 1 $. | 6 |
| 537 | Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = -30 ~~ \text{and} ~~ d = 10 $. | 6 |
| 538 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $. | 6 |
| 539 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $. | 6 |
| 540 | Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $. | 6 |
| 541 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $. | 6 |
| 542 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $. | 6 |
| 543 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 25 } ~~ \text{and} ~~ d = \frac{ 4 }{ 25 } $. | 6 |
| 544 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 2232141 }{ 50 } $. | 6 |
| 545 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = 6 $. | 6 |
| 546 | Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = -30 ~~ \text{and} ~~ d = 10 $. | 6 |
| 547 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = -1 $. | 6 |
| 548 | Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 8 $. | 6 |
| 549 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 6 |
| 550 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $. | 6 |
