Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 1451 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1452 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 8 $. | 4 |
| 1453 | Find $ a_{ 42 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $. | 4 |
| 1454 | $$ a_1 = 4 ~,~ d = \frac{ 1 }{ 4 } ~,~ a_n = 80 ~,~ n = ? $$ | 4 |
| 1455 | Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1456 | Find $ a_{ 69 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = 10 $. | 4 |
| 1457 | $$ a_1 = 3 ~~,~~ d = 6 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 4 |
| 1458 | Find $ S_{ 64 } $ ( sum of first $ 64 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 0 $. | 4 |
| 1459 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = \left( -10 \right) $. | 4 |
| 1460 | Find $ a_1 $ (first term of arithmetic progression) if $ d = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ a_{ 11 } = \frac{ 1 }{ 2 } $. | 4 |
| 1461 | Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -2 \right) $. | 4 |
| 1462 | Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $. | 4 |
| 1463 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1464 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 6 $. | 4 |
| 1465 | Find $ S_{ 66 } $ ( sum of first $ 66 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 15 $. | 4 |
| 1466 | Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = -\frac{ 16 }{ 25 } $. | 4 |
| 1467 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 7 $. | 4 |
| 1468 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 500 $. | 4 |
| 1469 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 2000 ~~ \text{and} ~~ d = 250 $. | 4 |
| 1470 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1471 | Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $. | 4 |
| 1472 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 89 $. | 4 |
| 1473 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 225 ~~ \text{and} ~~ d = \left( -29 \right) $. | 4 |
| 1474 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1475 | Find $ a_{ 61 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1476 | Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 7 $. | 4 |
| 1477 | $$ a_1 = 7 ~,~ d = 7 ~,~ S_n = 1477 ~,~ n = ? $$ | 4 |
| 1478 | Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1479 | Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 4 |
| 1480 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1481 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 1 $. | 4 |
| 1482 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 8 $. | 4 |
| 1483 | Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 6 $. | 4 |
| 1484 | Find $ S_{ 190 } $ ( sum of first $ 190 $ terms ) of arithmetic progression if $ a_1 = 72 ~~ \text{and} ~~ d = 1 $. | 4 |
| 1485 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = -2 $. | 4 |
| 1486 | $$ a_1 = 1 ~,~ d = 3 ~,~ S_n = 287 ~,~ n = ? $$ | 4 |
| 1487 | Find $ a_{ 74 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 0 $. | 4 |
| 1488 | Find $ a_{ 81 } $ of an arithmetic progression if $ a_1 = \frac{ 47 }{ 7 } ~~ \text{and} ~~ d = \left( -\frac{ 31 }{ 7 } \right) $. | 4 |
| 1489 | Find $ a_{ 88 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \frac{ 46 }{ 5 } $. | 4 |
| 1490 | Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 493 ~~ \text{and} ~~ d = \left( -\frac{ 65 }{ 2 } \right) $. | 4 |
| 1491 | Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = -18 ~~ \text{and} ~~ d = \left( -4 \right) $. | 4 |
| 1492 | Find $ a_{ 92 } $ of an arithmetic progression if $ a_1 = 27 ~~ \text{and} ~~ d = \left( -3 \right) $. | 4 |
| 1493 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $. | 4 |
| 1494 | Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 108 ~~ \text{and} ~~ d = \left( -2 \right) $. | 4 |
| 1495 | Find $ a_{ 65 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -3 \right) $. | 4 |
| 1496 | Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = \frac{ 39 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 11 }{ 2 } \right) $. | 4 |
| 1497 | Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = \frac{ 39 }{ 2 } ~~ \text{and} ~~ d = -\frac{ 11 }{ 2 } $. | 4 |
| 1498 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ d = \frac{ 7 }{ 3 } $. | 4 |
| 1499 | Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 1 $. | 4 |
| 1500 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 1 $. | 4 |
