Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 9801 | $$ a_1 = 3 ~,~ d = 4 ~,~ S_n = 210 ~,~ n = ? $$ | 1 |
| 9802 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 10 $. | 1 |
| 9803 | Find $ S_{ 10000 } $ ( sum of first $ 10000 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 4 $. | 1 |
| 9804 | Find $ a_{ 10000 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 4 $. | 1 |
| 9805 | Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $. | 1 |
| 9806 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = 37 $. | 1 |
| 9807 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 57 ~~ \text{and} ~~ d = 30 $. | 1 |
| 9808 | Find $ a_{ 86 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 14 $. | 1 |
| 9809 | Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $. | 1 |
| 9810 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 1000 $. | 1 |
| 9811 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 12 $. | 1 |
| 9812 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ S_{ 11 } = 231 $. | 1 |
| 9813 | Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $. | 1 |
| 9814 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 6 $. | 1 |
| 9815 | Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = -3 $. | 1 |
| 9816 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 75 ~~ \text{and} ~~ d = 18 $. | 1 |
| 9817 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 83 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 9818 | Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 83 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 9819 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 83 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 9820 | Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 83 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 9821 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = -52 ~~ \text{and} ~~ d = -3 $. | 1 |
| 9822 | $$ a_1 = -17 ~,~ d = 5 ~,~ a_n = 23 ~,~ n = ? $$ | 1 |
| 9823 | $$ a_1 = -17 ~,~ d = 5 ~,~ a_n = 33 ~,~ n = ? $$ | 1 |
| 9824 | $$ a_1 = 1 ~,~ d = \frac{ 1 }{ 4 } ~,~ a_n = \frac{ 39 }{ 4 } ~,~ n = ? $$ | 1 |
| 9825 | Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 4 $. | 1 |
| 9826 | Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 4 $. | 1 |
| 9827 | Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 5 $. | 1 |
| 9828 | Find $ a_1 $ (first term of arithmetic progression) if $ d = -6 ~~ \text{and} ~~ a_{ 30 } = -77 $. | 1 |
| 9829 | $$ a_1 = 1 ~,~ d = 2 ~,~ a_n = 71 ~,~ n = ? $$ | 1 |
| 9830 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 0 $. | 1 |
| 9831 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = 3 $. | 1 |
| 9832 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 9833 | Find $ a_{ 201 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
| 9834 | Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 1 |
| 9835 | Find $ a_{ 49 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $. | 1 |
| 9836 | Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = -7 $. | 1 |
| 9837 | Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -7 \right) $. | 1 |
| 9838 | Find $ S_{ 101 } $ ( sum of first $ 101 $ terms ) of arithmetic progression if $ a_1 = 504 ~~ \text{and} ~~ d = -5 $. | 1 |
| 9839 | Find $ a_{ 65 } $ of an arithmetic progression if $ a_1 = -30 ~~ \text{and} ~~ d = 11 $. | 1 |
| 9840 | Find $ a_{ 51 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $. | 1 |
| 9841 | Find $ S_{ 1305 } $ ( sum of first $ 1305 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 1 |
| 9842 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $. | 1 |
| 9843 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $. | 1 |
| 9844 | Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = -5 $. | 1 |
| 9845 | Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 9846 | Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 6 $. | 1 |
| 9847 | Find $ a_{ 54 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 4 $. | 1 |
| 9848 | Find $ S_{ 124 } $ ( sum of first $ 124 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 250 $. | 1 |
| 9849 | Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $. | 1 |
| 9850 | Find $ d $ (common difference of arithmetic progression) if $ a_1 = 6 ~~ \text{and} ~~ S_{ 2 } = 28 $. | 1 |
