Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 6701 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -7 \right) $. | 1 |
| 6702 | Find $ S_{ 23 } $ ( sum of first $ 23 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -7 $. | 1 |
| 6703 | $$ a_1 = \frac{ 91 }{ 10 } ~~,~~ d = \frac{ 8 }{ 5 } ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 6704 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -8 \right) $. | 1 |
| 6705 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = -8 $. | 1 |
| 6706 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 4250 ~~ \text{and} ~~ d = 100 $. | 1 |
| 6707 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 1996 ~~ \text{and} ~~ d = 0 $. | 1 |
| 6708 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 17 } ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $. | 1 |
| 6709 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 17 }{ 3 } ~~ \text{and} ~~ d = \frac{ 23 }{ 66 } $. | 1 |
| 6710 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = \frac{ 17 }{ 3 } ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $. | 1 |
| 6711 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = \frac{ 17 }{ 3 } ~~ \text{and} ~~ d = \frac{ 23 }{ 18 } $. | 1 |
| 6712 | Find common difference $ d $ of arithmetic progression if $ a_1 = \frac{ 17 }{ 3 } ~~ \text{and} ~~ a_{ 8 } = \frac{ 19 }{ 2 } $. | 1 |
| 6713 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 17 }{ 3 } ~~ \text{and} ~~ d = \frac{ 263 }{ 18 } $. | 1 |
| 6714 | Find common difference $ d $ of arithmetic progression if $ a_1 = \frac{ 17 }{ 3 } ~~ \text{and} ~~ a_{ 12 } = \frac{ 355 }{ 18 } $. | 1 |
| 6715 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 2100 ~~ \text{and} ~~ d = 150 $. | 1 |
| 6716 | Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 351 ~~ \text{and} ~~ d = 7 $. | 1 |
| 6717 | Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 12 $. | 1 |
| 6718 | Find $ S_{ 29 } $ ( sum of first $ 29 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = -2 $. | 1 |
| 6719 | $$ a_1 = \frac{ 1 }{ 2 } ~,~ d = \frac{ 7 }{ 2 } ~,~ a_n = 25 ~,~ n = ? $$ | 1 |
| 6720 | Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 7 }{ 2 } $. | 1 |
| 6721 | Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $. | 1 |
| 6722 | Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 12 $. | 1 |
| 6723 | Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $. | 1 |
| 6724 | Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 6 $. | 1 |
| 6725 | Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 1 |
| 6726 | Find common difference $ d $ of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ a_{ 5 } = 23 $. | 1 |
| 6727 | $$ a_{ 2 } = 6 ~~,~~ S_{ 5 } = 160 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 6728 | Find $ S_{ 27 } $ ( sum of first $ 27 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $. | 1 |
| 6729 | Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 545 ~~ \text{and} ~~ d = 64 $. | 1 |
| 6730 | $$ a_1 = \frac{ 1 }{ 5 } ~~,~~ d = \frac{ 1 }{ 2 } ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 6731 | $$ a_{ 2 } = \frac{ 7 }{ 10 } ~~,~~ S_{ 5 } = 6 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 6732 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 1 |
| 6733 | $$ a_1 = 76 ~~,~~ d = -6 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 6734 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 76 ~~ \text{and} ~~ d = \left( -6 \right) $. | 1 |
| 6735 | Find $ S_{ 1007 } $ ( sum of first $ 1007 $ terms ) of arithmetic progression if $ a_1 = 4029 ~~ \text{and} ~~ d = -4 $. | 1 |
| 6736 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 3 $. | 1 |
| 6737 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = \left( -5 \right) $. | 1 |
| 6738 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 2000 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6739 | Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 2001 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6740 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = -3 $. | 1 |
| 6741 | Find $ S_{ 51 } $ ( sum of first $ 51 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6742 | Find $ d $ (common difference of arithmetic progression) if $ a_1 = 3 ~~ \text{and} ~~ S_{ 30 } = 1860 $. | 1 |
| 6743 | Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $. | 1 |
| 6744 | Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -9 \right) $. | 1 |
| 6745 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = 4 $. | 1 |
| 6746 | $$ a_1 = 7 ~,~ d = 12 ~,~ a_n = 100 ~,~ n = ? $$ | 1 |
| 6747 | Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 13 $. | 1 |
| 6748 | Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 7 $. | 1 |
| 6749 | Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $. | 1 |
| 6750 | Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 129 ~~ \text{and} ~~ d = 1 $. | 1 |
