Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 9151 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $. | 1 |
| 9152 | Find $ a_3 $ of a geometric progression if $ a_1 = 90 ~~ \text{and} ~~ r = -4 $. | 1 |
| 9153 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $. | 1 |
| 9154 | Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 16 } ~~ \text{and} ~~ r = -4 $. | 1 |
| 9155 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = 6 $. | 1 |
| 9156 | Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $. | 1 |
| 9157 | Find $ a_7 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 2 } $. | 1 |
| 9158 | $$ a_1 = 8 ~,~ r = \frac{ 1 }{ 3 } ~,~ a_n = 8 ~,~ n = ? $$ | 1 |
| 9159 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 121 }{ 2 } ~~ \text{and} ~~ r = 2 $. | 1 |
| 9160 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 121 }{ 2 } ~~ \text{and} ~~ r = \frac{ 2 }{ 11 } $. | 1 |
| 9161 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 7 }{ 6 } ~~ \text{and} ~~ r = \dfrac{ 49 }{ 36 } $. | 1 |
| 9162 | Find $ a_4 $ of a geometric progression if $ a_1 = 264 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 9163 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = -\frac{ 3 }{ 2 } $. | 1 |
| 9164 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 1 |
| 9165 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 2 } = 24 ~~ \text{and} ~~ a_{ 5 } = 1536 $. | 1 |
| 9166 | Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 27 }{ 25 } $. | 1 |
| 9167 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 27 }{ 25 } $. | 1 |
| 9168 | Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.08 $. | 1 |
| 9169 | Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 24 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 9170 | Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9171 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -\frac{ 2 }{ 5 } $. | 1 |
| 9172 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 30 ~~ \text{and} ~~ r = -5 $. | 1 |
| 9173 | Find $ a_8 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9174 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 21 ~~ \text{and} ~~ r = -5 $. | 1 |
| 9175 | Find $ a_4 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9176 | Find $ a_6 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9177 | Find $ a_3 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9178 | Find $ a_9 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 9179 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 21 }{ 10 } ~~ \text{and} ~~ r = 2 $. | 1 |
| 9180 | Find $ a_4 $ of a geometric progression if $ a_1 = 67 ~~ \text{and} ~~ r = 13 $. | 1 |
| 9181 | Find $ a_5 $ of a geometric progression if $ a_1 = 360 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 8 } $. | 1 |
| 9182 | Find $ a_4 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -8 $. | 1 |
| 9183 | Find $ a_5 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -8 $. | 1 |
| 9184 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 0.5 ~~ \text{and} ~~ r = 0.5 $. | 1 |
| 9185 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 9186 | $$ a_1 = 2 ~~,~~ r = \frac{ 3 }{ 2 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 9187 | Find $ a_54 $ of a geometric progression if $ a_1 = 1025 ~~ \text{and} ~~ r = 8 $. | 1 |
| 9188 | Find $ a_58 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 9189 | Find $ a_3 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = 8 $. | 1 |
| 9190 | Find $ a_3 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = 0.9 $. | 1 |
| 9191 | Find $ a_45 $ of a geometric progression if $ a_1 = 152 ~~ \text{and} ~~ r = -3 $. | 1 |
| 9192 | $$ a_1 = 9 ~,~ r = \frac{ 3 }{ 5 } ~,~ a_n = 8 ~,~ n = ? $$ | 1 |
| 9193 | $$ a_1 = 5 ~,~ r = 2 ~,~ a_n = 2560 ~,~ n = ? $$ | 1 |
| 9194 | Find $ a_1 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 5 } ~~ \text{and} ~~ r = -1 $. | 1 |
| 9195 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.08 $. | 1 |
| 9196 | Find $ a_12 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 5 } ~~ \text{and} ~~ r = 5 $. | 1 |
| 9197 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -3 $. | 1 |
| 9198 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -3 $. | 1 |
| 9199 | Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 81 }{ 25 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $. | 1 |
| 9200 | Find $ a_4 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $. | 1 |
