Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 9501 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = -5 $. | 1 |
| 9502 | Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = -5 $. | 1 |
| 9503 | Find common difference $ d $ of arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ a_{ 15 } = 99 $. | 1 |
| 9504 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 0 $. | 1 |
| 9505 | $$ a_1 = 5 ~,~ d = 2 ~,~ S_n = 4 ~,~ n = ? $$ | 1 |
| 9506 | $$ a_{ 10 } = 120 ~~,~~ S_{ 30 } = 320 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 9507 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ d = \frac{ 1 }{ 10 } $. | 1 |
| 9508 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 14015 ~~ \text{and} ~~ d = \left( -260 \right) $. | 1 |
| 9509 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $. | 1 |
| 9510 | Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -5 \right) $. | 1 |
| 9511 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 25000 ~~ \text{and} ~~ d = 0 $. | 1 |
| 9512 | Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $. | 1 |
| 9513 | Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 0 $. | 1 |
| 9514 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \frac{ 15 }{ 4 } $. | 1 |
| 9515 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 3 $. | 1 |
| 9516 | $$ d = 2 ~,~ a_n = 2 ~,~ S_n = 1 ~,~ n = ? $$ | 1 |
| 9517 | $$ a_1 = 1 ~~,~~ d = \frac{ 7 }{ 2 } ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 9518 | Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 7 }{ 2 } $. | 1 |
| 9519 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 7 }{ 2 } $. | 1 |
| 9520 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 1 $. | 1 |
| 9521 | Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = -16 ~~ \text{and} ~~ d = 3 $. | 1 |
| 9522 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = -8 $. | 1 |
| 9523 | Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = 1 $. | 1 |
| 9524 | $$ a_1 = -5 ~~,~~ d = 5 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 9525 | Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $. | 1 |
| 9526 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $. | 1 |
| 9527 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 22 $. | 1 |
| 9528 | Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $. | 1 |
| 9529 | Find $ a_{ 51 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 13 $. | 1 |
| 9530 | Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = -27 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 9531 | $$ a_1 = 6 ~,~ d = 3 ~,~ a_n = 126 ~,~ n = ? $$ | 1 |
| 9532 | Find $ a_{ 61 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 6 $. | 1 |
| 9533 | Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 7 $. | 1 |
| 9534 | Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 1 $. | 1 |
| 9535 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -19 ~~ \text{and} ~~ d = 6 $. | 1 |
| 9536 | Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = 93 $. | 1 |
| 9537 | Find $ a_{ 46 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 4 $. | 1 |
| 9538 | Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 9539 | Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -5 \right) $. | 1 |
| 9540 | Find $ S_{ 44 } $ ( sum of first $ 44 $ terms ) of arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = -6 $. | 1 |
| 9541 | Find $ a_{ 110 } $ of an arithmetic progression if $ a_1 = 7456 ~~ \text{and} ~~ d = 64 $. | 1 |
| 9542 | Find $ S_{ 110 } $ ( sum of first $ 110 $ terms ) of arithmetic progression if $ a_1 = 7456 ~~ \text{and} ~~ d = 64 $. | 1 |
| 9543 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -18 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 9544 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 13 $. | 1 |
| 9545 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 250 ~~ \text{and} ~~ d = 37 $. | 1 |
| 9546 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 0 $. | 1 |
| 9547 | $$ a_1 = 5 ~,~ d = 5 ~,~ S_n = -4 ~,~ n = ? $$ | 1 |
| 9548 | $$ a_1 = \frac{ 1 }{ 2 } ~,~ d = 5 ~,~ a_n = 5 ~,~ n = ? $$ | 1 |
| 9549 | Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = 78 ~~ \text{and} ~~ d = 4 $. | 1 |
| 9550 | Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = 78 ~~ \text{and} ~~ d = 0 $. | 1 |
