Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 7751 | Find common difference $ d $ of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ a_{ 5 } = 19 $. | 1 |
| 7752 | Find $ a_{ 1600 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 14 $. | 1 |
| 7753 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $. | 1 |
| 7754 | $$ a_{ 9 } = -13 ~~,~~ S_{ 37 } = -1591 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 7755 | Find $ a_{ 78 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $. | 1 |
| 7756 | Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 10 $. | 1 |
| 7757 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = -\frac{ 5 }{ 4 } ~~ \text{and} ~~ d = \left( -1 \right) $. | 1 |
| 7758 | Find $ S_{ 543 } $ ( sum of first $ 543 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7759 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 7760 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 5 $. | 1 |
| 7761 | $$ a_1 = 2 ~,~ d = \frac{ 1 }{ 2 } ~,~ a_n = 99 ~,~ n = ? $$ | 1 |
| 7762 | Find $ a_{ 44 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7763 | Find $ a_{ 67 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 6 $. | 1 |
| 7764 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7765 | Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = -18 ~~ \text{and} ~~ d = 14 $. | 1 |
| 7766 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = -\frac{ 3 }{ 2 } $. | 1 |
| 7767 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = \frac{ 17 }{ 10 } ~~ \text{and} ~~ d = \left( -\frac{ 3 }{ 10 } \right) $. | 1 |
| 7768 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 68 ~~ \text{and} ~~ d = 7 $. | 1 |
| 7769 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 68 ~~ \text{and} ~~ d = 7 $. | 1 |
| 7770 | Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = \frac{ 5 }{ 4 } ~~ \text{and} ~~ d = \frac{ 5 }{ 4 } $. | 1 |
| 7771 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 4 } ~~ \text{and} ~~ d = \frac{ 5 }{ 4 } $. | 1 |
| 7772 | Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7773 | Find $ S_{ 56 } $ ( sum of first $ 56 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 5 $. | 1 |
| 7774 | Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $. | 1 |
| 7775 | Find $ a_{ 66 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7776 | Find $ a_{ 56 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 9 $. | 1 |
| 7777 | Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = \left( -10 \right) $. | 1 |
| 7778 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7779 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 5 $. | 1 |
| 7780 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 950 ~~ \text{and} ~~ d = 55 $. | 1 |
| 7781 | Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7782 | Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7783 | Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7784 | Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 7 $. | 1 |
| 7785 | Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 7 $. | 1 |
| 7786 | Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 1 |
| 7787 | Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = -36 ~~ \text{and} ~~ d = \left( -10 \right) $. | 1 |
| 7788 | $$ a_1 = 5 ~,~ d = \frac{ 1 }{ 2 } ~,~ a_n = \frac{ 189 }{ 2 } ~,~ n = ? $$ | 1 |
| 7789 | Find $ S_{ 180 } $ ( sum of first $ 180 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 1 |
| 7790 | Find $ S_{ 39 } $ ( sum of first $ 39 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 6 $. | 1 |
| 7791 | Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = -34 ~~ \text{and} ~~ d = \left( -8 \right) $. | 1 |
| 7792 | Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 100 $. | 1 |
| 7793 | Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7794 | Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 27 ~~ \text{and} ~~ d = \left( -10 \right) $. | 1 |
| 7795 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 100 $. | 1 |
| 7796 | $$ a_1 = 30000 ~,~ d = 1200 ~,~ S_n = 483600 ~,~ n = ? $$ | 1 |
| 7797 | $$ a_1 = 27 ~,~ a_n = 57 ~,~ S_n = 462 ~,~ n = ? $$ | 1 |
| 7798 | $$ a_1 = -2 ~,~ a_n = 42 ~,~ S_n = 360 ~,~ n = ? $$ | 1 |
| 7799 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 7 ~~ \text{and} ~~ S_{ 9 } = 378 $. | 1 |
| 7800 | Find $ a_{ 78 } $ of an arithmetic progression if $ a_1 = -894 ~~ \text{and} ~~ d = 15 $. | 1 |
