Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 701 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 4 }{ 3 } $. | 5 |
| 702 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 4 }{ 3 } $. | 5 |
| 703 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 1 $. | 5 |
| 704 | Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ d = 0.001 $. | 5 |
| 705 | Find $ S_{ 20000 } $ ( sum of first $ 20000 $ terms ) of arithmetic progression if $ a_1 = 0.001 ~~ \text{and} ~~ d = 1.0E-5 $. | 5 |
| 706 | Find $ S_{ 2000 } $ ( sum of first $ 2000 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $. | 5 |
| 707 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 4000 ~~ \text{and} ~~ d = 300 $. | 5 |
| 708 | Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $. | 5 |
| 709 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 11 } ~~ \text{and} ~~ d = \frac{ 4 }{ 11 } $. | 5 |
| 710 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = 0 $. | 5 |
| 711 | $$ a_1 = -21 ~~,~~ d = 100 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 5 |
| 712 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 97 ~~ \text{and} ~~ d = 4 $. | 5 |
| 713 | Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 7 $. | 5 |
| 714 | Find $ a_{ 98 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 16 $. | 5 |
| 715 | Find $ S_{ 23 } $ ( sum of first $ 23 $ terms ) of arithmetic progression if $ a_1 = 120 ~~ \text{and} ~~ d = 5 $. | 5 |
| 716 | Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 120 ~~ \text{and} ~~ d = 5 $. | 5 |
| 717 | Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 320 ~~ \text{and} ~~ d = 5 $. | 5 |
| 718 | $$ a_1 = 1 ~,~ d = 8 ~,~ a_n = 89 ~,~ n = ? $$ | 5 |
| 719 | Find $ S_{ 89 } $ ( sum of first $ 89 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 8 $. | 5 |
| 720 | Find $ S_{ 93 } $ ( sum of first $ 93 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 8 $. | 5 |
| 721 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 8 ~~ \text{and} ~~ a_{ 9 } = 81 $. | 5 |
| 722 | Find $ S_{ 89 } $ ( sum of first $ 89 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 8 $. | 5 |
| 723 | $$ a_1 = 231 ~,~ d = 7 ~,~ a_n = 50 ~,~ n = ? $$ | 5 |
| 724 | Find $ S_{ 66 } $ ( sum of first $ 66 $ terms ) of arithmetic progression if $ a_1 = 231 ~~ \text{and} ~~ d = 7 $. | 5 |
| 725 | Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 231 ~~ \text{and} ~~ d = 28 $. | 5 |
| 726 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 6 $. | 5 |
| 727 | Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = \left( -4 \right) $. | 5 |
| 728 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -7 $. | 5 |
| 729 | Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -4 \right) $. | 5 |
| 730 | Find $ S_{ 500 } $ ( sum of first $ 500 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $. | 5 |
| 731 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $. | 5 |
| 732 | Find $ a_{ 109 } $ of an arithmetic progression if $ a_1 = 963 ~~ \text{and} ~~ d = 27 $. | 5 |
| 733 | Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $. | 5 |
| 734 | Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $. | 5 |
| 735 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 1 $. | 5 |
| 736 | $$ a_1 = 1 ~,~ d = 1 ~,~ S_n = 6205 ~,~ n = ? $$ | 5 |
| 737 | Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = -100 ~~ \text{and} ~~ d = 10 $. | 5 |
| 738 | Find $ a_{ 47 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 5 |
| 739 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 6 $. | 5 |
| 740 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 181 ~~ \text{and} ~~ d = 4 $. | 5 |
| 741 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $. | 5 |
| 742 | Find $ a_{ 81 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 4 $. | 5 |
| 743 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -5 \right) $. | 5 |
| 744 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 20 $. | 5 |
| 745 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 12 $. | 5 |
| 746 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 13000 ~~ \text{and} ~~ d = 900 $. | 5 |
| 747 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 5 |
| 748 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 8 $. | 5 |
| 749 | Find $ a_{ 999 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 5 |
| 750 | Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -3 \right) $. | 5 |
