Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 7701 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 21 }{ 20 } $. | 1 |
| 7702 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 7 $. | 1 |
| 7703 | $$ a_1 = 1 ~,~ d = 3 ~,~ a_n = 52 ~,~ n = ? $$ | 1 |
| 7704 | Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = -40 ~~ \text{and} ~~ d = 10 $. | 1 |
| 7705 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 7500 ~~ \text{and} ~~ d = 225 $. | 1 |
| 7706 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 6 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $. | 1 |
| 7707 | Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7708 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $. | 1 |
| 7709 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 7 $. | 1 |
| 7710 | $$ a_1 = 72000 ~,~ d = 18000 ~,~ S_n = 3312000 ~,~ n = ? $$ | 1 |
| 7711 | $$ a_1 = 1 ~,~ d = 3 ~,~ a_n = 68 ~,~ n = ? $$ | 1 |
| 7712 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 6 $. | 1 |
| 7713 | Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = \frac{ 47 }{ 10 } ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 7714 | Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7715 | Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = -\frac{ 11 }{ 5 } ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $. | 1 |
| 7716 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = -2 $. | 1 |
| 7717 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = -5 $. | 1 |
| 7718 | Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = \frac{ 17 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $. | 1 |
| 7719 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 8 } \right) $. | 1 |
| 7720 | Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 5000 $. | 1 |
| 7721 | Find $ S_{ 55 } $ ( sum of first $ 55 $ terms ) of arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7722 | $$ a_{ 6 } = -4 ~~,~~ S_{ 10 } = -28 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 7723 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7724 | Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 6 $. | 1 |
| 7725 | Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = -25 ~~ \text{and} ~~ d = 6 $. | 1 |
| 7726 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 7727 | Find $ S_{ 500 } $ ( sum of first $ 500 $ terms ) of arithmetic progression if $ a_1 = 50000 ~~ \text{and} ~~ d = 300 $. | 1 |
| 7728 | Find $ a_{ 500 } $ of an arithmetic progression if $ a_1 = 50000 ~~ \text{and} ~~ d = 300 $. | 1 |
| 7729 | Find $ a_{ 501 } $ of an arithmetic progression if $ a_1 = 50000 ~~ \text{and} ~~ d = 300 $. | 1 |
| 7730 | Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7731 | Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 2 $. | 1 |
| 7732 | Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = -100000 ~~ \text{and} ~~ d = 1000 $. | 1 |
| 7733 | Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = -1000000 ~~ \text{and} ~~ d = 1000 $. | 1 |
| 7734 | Find $ a_{ 192 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $. | 1 |
| 7735 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = -2 $. | 1 |
| 7736 | Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 6 $. | 1 |
| 7737 | $$ a_1 = 5 ~~,~~ d = 1 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 7738 | Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = -5 $. | 1 |
| 7739 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7740 | Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = -\frac{ 31 }{ 100 } ~~ \text{and} ~~ d = \frac{ 89 }{ 50 } $. | 1 |
| 7741 | Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7742 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7743 | Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 120 ~~ \text{and} ~~ d = -1 $. | 1 |
| 7744 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -\frac{ 7 }{ 3 } ~~ \text{and} ~~ d = \left( -\frac{ 2 }{ 3 } \right) $. | 1 |
| 7745 | Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 7 $. | 1 |
| 7746 | Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = -53 ~~ \text{and} ~~ d = 13 $. | 1 |
| 7747 | Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 79 ~~ \text{and} ~~ d = 0 $. | 1 |
| 7748 | Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = -16 ~~ \text{and} ~~ d = 6 $. | 1 |
| 7749 | Find $ a_{ 42 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 5 $. | 1 |
| 7750 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
