Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 7601 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 10 $. | 1 |
| 7602 | Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7603 | Find $ a_{ 500 } $ of an arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7604 | Find $ a_{ 500 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7605 | $$ a_1 = -1 ~,~ a_n = 45 ~,~ S_n = 440 ~,~ n = ? $$ | 1 |
| 7606 | Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 1222 ~~ \text{and} ~~ d = 8 $. | 1 |
| 7607 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 253 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 7608 | Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 203 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7609 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 10 $. | 1 |
| 7610 | $$ a_1 = 13 ~,~ d = 8 ~,~ S_n = 1222 ~,~ n = ? $$ | 1 |
| 7611 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 1 |
| 7612 | Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 206 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 7613 | Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 360 ~~ \text{and} ~~ d = \left( -7 \right) $. | 1 |
| 7614 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 8 ~~ \text{and} ~~ a_{ 13 } = 1222 $. | 1 |
| 7615 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 8 ~~ \text{and} ~~ S_{ 13 } = 1222 $. | 1 |
| 7616 | $$ a_1 = 42 ~,~ a_n = 112 ~,~ S_n = 847 ~,~ n = ? $$ | 1 |
| 7617 | Find common difference $ d $ of arithmetic progression if $ a_1 = -56 ~~ \text{and} ~~ a_{ 36 } = 364 $. | 1 |
| 7618 | Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = -56 ~~ \text{and} ~~ d = 12 $. | 1 |
| 7619 | Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = -90 ~~ \text{and} ~~ d = 13 $. | 1 |
| 7620 | Find $ a_{ 55 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 1 }{ 6 } $. | 1 |
| 7621 | $$ a_{ 32 } = 257 ~~,~~ S_{ 32 } = 3264 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 7622 | $$ a_1 = 74 ~~,~~ d = 3 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 7623 | Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = -1 $. | 1 |
| 7624 | Find common difference $ d $ of arithmetic progression if $ a_1 = -58 ~~ \text{and} ~~ a_{ 35 } = 350 $. | 1 |
| 7625 | Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = -11 $. | 1 |
| 7626 | Find $ S_{ 55 } $ ( sum of first $ 55 $ terms ) of arithmetic progression if $ a_1 = 590 ~~ \text{and} ~~ d = 5 $. | 1 |
| 7627 | Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 7628 | Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7629 | Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 0 $. | 1 |
| 7630 | Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 50 } ~~ \text{and} ~~ d = 2 $. | 1 |
| 7631 | Find common difference $ d $ of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ a_{ 3 } = 7 $. | 1 |
| 7632 | $$ a_1 = 2 ~,~ d = \frac{ 2 }{ 5 } ~,~ a_n = 2 ~,~ n = ? $$ | 1 |
| 7633 | $$ a_1 = 625 ~,~ a_n = 6 ~,~ S_n = \frac{ 243 }{ 5 } ~,~ n = ? $$ | 1 |
| 7634 | Find common difference $ d $ of arithmetic progression if $ a_1 = 625 ~~ \text{and} ~~ a_{ 6 } = \frac{ 243 }{ 5 } $. | 1 |
| 7635 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 0 $. | 1 |
| 7636 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -5 \right) $. | 1 |
| 7637 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = \left( -8 \right) $. | 1 |
| 7638 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = -4 $. | 1 |
| 7639 | Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 5 $. | 1 |
| 7640 | Find $ a_{ 67 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7641 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7642 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7643 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7644 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 2 $. | 1 |
| 7645 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $. | 1 |
| 7646 | Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 7647 | Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 2 $. | 1 |
| 7648 | $$ a_1 = 4 ~~,~~ d = 5 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 7649 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 250 ~~ \text{and} ~~ d = \left( -25 \right) $. | 1 |
| 7650 | Find $ a_{ 76 } $ of an arithmetic progression if $ a_1 = 76 ~~ \text{and} ~~ d = 2 $. | 1 |
