Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 1601 | Find $ S_{ 400 } $ ( sum of first $ 400 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1602 | $$ a_1 = 97 ~,~ d = 1 ~,~ a_n = 146 ~,~ n = ? $$ | 4 |
| 1603 | $$ a_1 = 2 ~,~ d = 1 ~,~ a_n = 20 ~,~ n = ? $$ | 4 |
| 1604 | Find $ S_{ 3700 } $ ( sum of first $ 3700 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $. | 4 |
| 1605 | $$ a_{ 3 } = 12 ~~,~~ S_{ 17 } = 28 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 4 |
| 1606 | Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 7 $. | 4 |
| 1607 | Find $ a_{ 89 } $ of an arithmetic progression if $ a_1 = 2010 ~~ \text{and} ~~ d = 1 $. | 4 |
| 1608 | Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = 2010 ~~ \text{and} ~~ d = 1 $. | 4 |
| 1609 | Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -4 \right) $. | 4 |
| 1610 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1611 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = 57 $. | 4 |
| 1612 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $. | 4 |
| 1613 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 0 $. | 4 |
| 1614 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1615 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1616 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1617 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = 6 $. | 4 |
| 1618 | Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 0 $. | 4 |
| 1619 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 63 ~~ \text{and} ~~ d = \left( -10 \right) $. | 4 |
| 1620 | Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1621 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 5 $. | 4 |
| 1622 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 4 } \right) $. | 4 |
| 1623 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 1 $. | 4 |
| 1624 | Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 1 $. | 4 |
| 1625 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 253 $. | 4 |
| 1626 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 254 $. | 4 |
| 1627 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 255 $. | 4 |
| 1628 | Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1629 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 8 } ~~ \text{and} ~~ d = \frac{ 1 }{ 8 } $. | 4 |
| 1630 | Find $ S_{ 2024 } $ ( sum of first $ 2024 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $. | 4 |
| 1631 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -5 \right) $. | 4 |
| 1632 | Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 11 $. | 4 |
| 1633 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 0.625 ~~ \text{and} ~~ d = -4 $. | 4 |
| 1634 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1635 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1636 | Find $ a_{ 255 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 25 $. | 4 |
| 1637 | Find $ S_{ 255 } $ ( sum of first $ 255 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 25 $. | 4 |
| 1638 | Find $ a_{ 43 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -5 \right) $. | 4 |
| 1639 | $$ a_1 = 60000000 ~,~ a_n = 200000000 ~,~ S_n = 60000000000 ~,~ n = ? $$ | 4 |
| 1640 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 200 $. | 4 |
| 1641 | Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1642 | Find $ S_{ 298 } $ ( sum of first $ 298 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1643 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 1000 $. | 4 |
| 1644 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 4862 ~~ \text{and} ~~ d = 0 $. | 4 |
| 1645 | $$ a_1 = 179 ~,~ d = 39 ~,~ S_n = 69941 ~,~ n = ? $$ | 4 |
| 1646 | $$ a_1 = 25 ~,~ d = -6 ~,~ S_n = -20 ~,~ n = ? $$ | 4 |
| 1647 | Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 7 $. | 4 |
| 1648 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1649 | Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 18000 ~~ \text{and} ~~ d = \left( -500 \right) $. | 4 |
| 1650 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 18000 ~~ \text{and} ~~ d = 500 $. | 4 |
