Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 8601 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $. | 1 |
| 8602 | Find $ a_{ 74 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 8 $. | 1 |
| 8603 | Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = -2 $. | 1 |
| 8604 | Find $ d $ (common difference of arithmetic progression) if $ a_1 = 6 ~~ \text{and} ~~ S_{ 9 } = 108 $. | 1 |
| 8605 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $. | 1 |
| 8606 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 8607 | Find $ S_{ 44 } $ ( sum of first $ 44 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 1 |
| 8608 | Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 1 |
| 8609 | Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 1 |
| 8610 | Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 30 $. | 1 |
| 8611 | Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 30 $. | 1 |
| 8612 | Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = -\frac{ 7 }{ 20 } ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 8613 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 1 |
| 8614 | $$ a_1 = 3 ~,~ d = \frac{ 5 }{ 2 } ~,~ a_n = 133 ~,~ n = ? $$ | 1 |
| 8615 | Find $ S_{ 53 } $ ( sum of first $ 53 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $. | 1 |
| 8616 | Find $ S_{ 42 } $ ( sum of first $ 42 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 0 $. | 1 |
| 8617 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = -4 $. | 1 |
| 8618 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $. | 1 |
| 8619 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $. | 1 |
| 8620 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = -8 $. | 1 |
| 8621 | Find $ S_{ 29 } $ ( sum of first $ 29 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = -8 $. | 1 |
| 8622 | Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 75 ~~ \text{and} ~~ d = 8 $. | 1 |
| 8623 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 75 ~~ \text{and} ~~ d = 8 $. | 1 |
| 8624 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -10 \right) $. | 1 |
| 8625 | $$ a_{ 16 } = 60 ~~,~~ S_{ 15 } = 540 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 8626 | Find $ S_{ 150 } $ ( sum of first $ 150 $ terms ) of arithmetic progression if $ a_1 = 102 ~~ \text{and} ~~ d = 6 $. | 1 |
| 8627 | Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 7 $. | 1 |
| 8628 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $. | 1 |
| 8629 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $. | 1 |
| 8630 | $$ a_1 = 50 ~,~ d = -4 ~,~ a_n = -34 ~,~ n = ? $$ | 1 |
| 8631 | $$ a_1 = 50 ~,~ d = -3 ~,~ a_n = -34 ~,~ n = ? $$ | 1 |
| 8632 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 3 $. | 1 |
| 8633 | Find $ a_{ 90 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = \left( -8 \right) $. | 1 |
| 8634 | $$ a_1 = 8 ~,~ d = 3 ~,~ a_n = 59 ~,~ n = ? $$ | 1 |
| 8635 | $$ a_1 = \frac{ 3 }{ 2 } ~,~ d = \frac{ 3 }{ 4 } ~,~ a_n = \frac{ 39 }{ 4 } ~,~ n = ? $$ | 1 |
| 8636 | Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $. | 1 |
| 8637 | Find $ S_{ 94 } $ ( sum of first $ 94 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 250 $. | 1 |
| 8638 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 51 ~~ \text{and} ~~ d = 10 $. | 1 |
| 8639 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 4 $. | 1 |
| 8640 | Find $ a_{ 101 } $ of an arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 250 $. | 1 |
| 8641 | Find $ S_{ 101 } $ ( sum of first $ 101 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 250 $. | 1 |
| 8642 | $$ a_1 = 60000 ~,~ d = 10000 ~,~ a_n = 200000 ~,~ n = ? $$ | 1 |
| 8643 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 3 $. | 1 |
| 8644 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 3 $. | 1 |
| 8645 | Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 3 $. | 1 |
| 8646 | Find $ S_{ 65 } $ ( sum of first $ 65 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 1 }{ 10 } $. | 1 |
| 8647 | Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = 1 $. | 1 |
| 8648 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 11 $. | 1 |
| 8649 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 11 $. | 1 |
| 8650 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = -13 $. | 1 |
