Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 6651 | Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 6 } $. | 1 |
| 6652 | Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = 6 $. | 1 |
| 6653 | Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = -23 ~~ \text{and} ~~ d = \left( -7 \right) $. | 1 |
| 6654 | Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = -23 ~~ \text{and} ~~ d = 7 $. | 1 |
| 6655 | Find $ a_{ 91 } $ of an arithmetic progression if $ a_1 = 96 ~~ \text{and} ~~ d = 7 $. | 1 |
| 6656 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6657 | Find $ a_{ 49 } $ of an arithmetic progression if $ a_1 = 41 ~~ \text{and} ~~ d = 2 $. | 1 |
| 6658 | Find $ S_{ 49 } $ ( sum of first $ 49 $ terms ) of arithmetic progression if $ a_1 = 41 ~~ \text{and} ~~ d = 2 $. | 1 |
| 6659 | Find $ a_{ 98 } $ of an arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6660 | Find $ S_{ 98 } $ ( sum of first $ 98 $ terms ) of arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6661 | Find $ S_{ 98 } $ ( sum of first $ 98 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 2308 }{ 49 } ~~ \text{and} ~~ d = 1 $. | 1 |
| 6662 | Find $ S_{ 49 } $ ( sum of first $ 49 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 2259 }{ 49 } ~~ \text{and} ~~ d = 2 $. | 1 |
| 6663 | Find $ S_{ 53 } $ ( sum of first $ 53 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6664 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 8 $. | 1 |
| 6665 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $. | 1 |
| 6666 | Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 6 $. | 1 |
| 6667 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 167 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 7 }{ 2 } \right) $. | 1 |
| 6668 | Find $ S_{ 499 } $ ( sum of first $ 499 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $. | 1 |
| 6669 | Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 8 $. | 1 |
| 6670 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = -6 $. | 1 |
| 6671 | Find $ a_{ 98 } $ of an arithmetic progression if $ a_1 = -\frac{ 2308 }{ 49 } ~~ \text{and} ~~ d = 1 $. | 1 |
| 6672 | $$ a_1 = -15 ~,~ d = 6 ~,~ a_n = 21 ~,~ n = ? $$ | 1 |
| 6673 | $$ a_1 = -15 ~,~ d = 6 ~,~ a_n = 1200 ~,~ n = ? $$ | 1 |
| 6674 | $$ a_1 = 6 ~,~ d = -9 ~,~ S_n = 1200 ~,~ n = ? $$ | 1 |
| 6675 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 83 ~~ \text{and} ~~ d = 6 $. | 1 |
| 6676 | Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 10 $. | 1 |
| 6677 | Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 10 $. | 1 |
| 6678 | Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 10 $. | 1 |
| 6679 | Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 10 $. | 1 |
| 6680 | Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 10 $. | 1 |
| 6681 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 10 $. | 1 |
| 6682 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = \frac{ 27 }{ 7 } ~~ \text{and} ~~ d = -\frac{ 5 }{ 7 } $. | 1 |
| 6683 | Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = \frac{ 22 }{ 7 } ~~ \text{and} ~~ d = -\frac{ 10 }{ 7 } $. | 1 |
| 6684 | Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = \frac{ 33 }{ 5 } ~~ \text{and} ~~ d = -\frac{ 10 }{ 7 } $. | 1 |
| 6685 | $$ a_{ 10 } = 13 ~~,~~ S_{ 11 } = 33 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 6686 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $. | 1 |
| 6687 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $. | 1 |
| 6688 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 0 $. | 1 |
| 6689 | Find common difference $ d $ of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ a_{ 3 } = 10 $. | 1 |
| 6690 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 8 $. | 1 |
| 6691 | $$ a_1 = -6 ~,~ d = 8 ~,~ S_n = 114 ~,~ n = ? $$ | 1 |
| 6692 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 64 ~~ \text{and} ~~ d = \left( -5 \right) $. | 1 |
| 6693 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 44 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6694 | Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 3 $. | 1 |
| 6695 | Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ d = \frac{ 1 }{ 50 } $. | 1 |
| 6696 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ d = \frac{ 1 }{ 50 } $. | 1 |
| 6697 | Find common difference $ d $ of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ a_{ 50 } = 331 $. | 1 |
| 6698 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \frac{ 46 }{ 7 } $. | 1 |
| 6699 | Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 11600 ~~ \text{and} ~~ d = 1000 $. | 1 |
| 6700 | Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 117000 ~~ \text{and} ~~ d = 500 $. | 1 |
