Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 8101 | $$ a_1 = 2 ~,~ d = 2 ~,~ a_n = 98 ~,~ n = ? $$ | 1 |
| 8102 | $$ a_1 = 1 ~,~ d = 2 ~,~ a_n = 51 ~,~ n = ? $$ | 1 |
| 8103 | $$ a_1 = 2 ~,~ d = 2 ~,~ a_n = 202 ~,~ n = ? $$ | 1 |
| 8104 | $$ a_1 = 1 ~,~ d = 2 ~,~ S_n = 100 ~,~ n = ? $$ | 1 |
| 8105 | | 1 |
| 8106 | $$ a_1 = 25 ~~,~~ d = -4 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 8107 | Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $. | 1 |
| 8108 | Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 68 ~~ \text{and} ~~ d = -\frac{ 16 }{ 5 } $. | 1 |
| 8109 | Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = -\frac{ 32 }{ 5 } $. | 1 |
| 8110 | Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 67 ~~ \text{and} ~~ d = -8 $. | 1 |
| 8111 | Find $ S_{ 42 } $ ( sum of first $ 42 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = -\frac{ 3 }{ 25 } $. | 1 |
| 8112 | Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = -\frac{ 4 }{ 5 } $. | 1 |
| 8113 | Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 51 ~~ \text{and} ~~ d = -\frac{ 8 }{ 5 } $. | 1 |
| 8114 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $. | 1 |
| 8115 | Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $. | 1 |
| 8116 | Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 3 $. | 1 |
| 8117 | Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = \left( -6 \right) $. | 1 |
| 8118 | Find $ a_{ 798 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 66 $. | 1 |
| 8119 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 56 ~~ \text{and} ~~ d = 43 $. | 1 |
| 8120 | Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 56 ~~ \text{and} ~~ d = 43 $. | 1 |
| 8121 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 120 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 8122 | Find $ a_{ 42 } $ of an arithmetic progression if $ a_1 = 120 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 8123 | $$ a_{ 12 } = 15 ~~,~~ S_{ 15 } = 105 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 8124 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 6 $. | 1 |
| 8125 | Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = \left( -7 \right) $. | 1 |
| 8126 | Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 9 $. | 1 |
| 8127 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 8128 | Find $ d $ (common difference of arithmetic progression) if $ a_1 = \frac{ 55 }{ 2 } ~~ \text{and} ~~ S_{ 16 } = 920 $. | 1 |
| 8129 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 11 ~~ \text{and} ~~ S_{ 16 } = 920 $. | 1 |
| 8130 | Find $ a_1 $ (first term of arithmetic progression) if $ d = \frac{ 55 }{ 2 } ~~ \text{and} ~~ S_{ 16 } = 920 $. | 1 |
| 8131 | Find common difference $ d $ of arithmetic progression if $ a_1 = 80 ~~ \text{and} ~~ a_{ 4 } = 10 $. | 1 |
| 8132 | Find common difference $ d $ of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ a_{ 7 } = 44 $. | 1 |
| 8133 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ a_{ 4 } = 20 $. | 1 |
| 8134 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $. | 1 |
| 8135 | Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $. | 1 |
| 8136 | Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $. | 1 |
| 8137 | Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $. | 1 |
| 8138 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $. | 1 |
| 8139 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $. | 1 |
| 8140 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = -1 $. | 1 |
| 8141 | $$ a_1 = 200 ~,~ d = 60 ~,~ S_n = 37290 ~,~ n = ? $$ | 1 |
| 8142 | Find $ S_{ 96 } $ ( sum of first $ 96 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 4 $. | 1 |
| 8143 | Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 4 $. | 1 |
| 8144 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = 10 $. | 1 |
| 8145 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -14 \right) $. | 1 |
| 8146 | Find $ S_{ 163 } $ ( sum of first $ 163 $ terms ) of arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 6 $. | 1 |
| 8147 | Find $ S_{ 998 } $ ( sum of first $ 998 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $. | 1 |
| 8148 | Find $ S_{ 998 } $ ( sum of first $ 998 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $. | 1 |
| 8149 | Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 30 $. | 1 |
| 8150 | Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 30 $. | 1 |
