Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 801 | Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = 30 $. | 5 |
| 802 | Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 100 $. | 5 |
| 803 | Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 9 $. | 5 |
| 804 | Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = -\frac{ 9 }{ 5 } ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $. | 5 |
| 805 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 9 $. | 5 |
| 806 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = \left( -7 \right) $. | 5 |
| 807 | Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 95 ~~ \text{and} ~~ d = \left( -6 \right) $. | 5 |
| 808 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = 10 $. | 5 |
| 809 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $. | 5 |
| 810 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -2 \right) $. | 5 |
| 811 | Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $. | 5 |
| 812 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 65 ~~ \text{and} ~~ d = \left( -7 \right) $. | 5 |
| 813 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 3 $. | 5 |
| 814 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = \left( -3 \right) $. | 5 |
| 815 | Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = \left( -20 \right) $. | 5 |
| 816 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = 9 $. | 5 |
| 817 | Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = 0 $. | 5 |
| 818 | Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 87 ~~ \text{and} ~~ d = \left( -4 \right) $. | 5 |
| 819 | Find $ a_{ 54 } $ of an arithmetic progression if $ a_1 = \frac{ 15 }{ 8 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 5 |
| 820 | Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 59 ~~ \text{and} ~~ d = -7 $. | 5 |
| 821 | Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = \frac{ 4 }{ 15 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 5 } \right) $. | 5 |
| 822 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 7 $. | 5 |
| 823 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 3 $. | 5 |
| 824 | Find $ a_{ 200000001 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 5 |
| 825 | Find $ a_{ 81 } $ of an arithmetic progression if $ a_1 = -28 ~~ \text{and} ~~ d = \left( -6 \right) $. | 5 |
| 826 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $. | 5 |
| 827 | Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 1800000 ~~ \text{and} ~~ d = 60000 $. | 5 |
| 828 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 1800000 ~~ \text{and} ~~ d = 60000 $. | 5 |
| 829 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 6 $. | 5 |
| 830 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 12 $. | 5 |
| 831 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 5 $. | 5 |
| 832 | Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 1800000 ~~ \text{and} ~~ d = 600000 $. | 5 |
| 833 | $$ a_1 = 10 ~,~ d = 10 ~,~ S_n = 60 ~,~ n = ? $$ | 5 |
| 834 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 25000 ~~ \text{and} ~~ d = 2500 $. | 5 |
| 835 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 1100 ~~ \text{and} ~~ d = 60 $. | 5 |
| 836 | Find $ S_{ 201 } $ ( sum of first $ 201 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 5 |
| 837 | Find $ a_{ 87 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 12 $. | 5 |
| 838 | $$ a_1 = 3 ~,~ d = 6 ~,~ a_n = 15 ~,~ n = ? $$ | 5 |
| 839 | Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = 190 ~~ \text{and} ~~ d = 190 $. | 5 |
| 840 | Find $ S_{ 750 } $ ( sum of first $ 750 $ terms ) of arithmetic progression if $ a_1 = 190 ~~ \text{and} ~~ d = 190 $. | 5 |
| 841 | $$ a_{ 10 } = 7 ~~,~~ S_{ 10 } = 64 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 5 |
| 842 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 8 } ~~ \text{and} ~~ d = \frac{ 1 }{ 8 } $. | 5 |
| 843 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -3 \right) $. | 5 |
| 844 | Find $ a_{ 106 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 19 $. | 5 |
| 845 | $$ a_{ 40 } = 40 ~~,~~ S_{ 40 } = 40 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 5 |
| 846 | Find $ d $ (common difference of arithmetic progression) if $ a_1 = -7 ~~ \text{and} ~~ S_{ 20 } = 1000 $. | 5 |
| 847 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 6 $. | 5 |
| 848 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 321 ~~ \text{and} ~~ d = 3 $. | 5 |
| 849 | Find $ a_{ 93 } $ of an arithmetic progression if $ a_1 = 2010 ~~ \text{and} ~~ d = 1 $. | 5 |
| 850 | Find $ S_{ 94 } $ ( sum of first $ 94 $ terms ) of arithmetic progression if $ a_1 = 2010 ~~ \text{and} ~~ d = 1 $. | 5 |
