Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 2151 | Find $ a_6 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = 3 $. | 4 |
| 2152 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 4 |
| 2153 | Find $ a_9 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -2 $. | 4 |
| 2154 | Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 9 $. | 4 |
| 2155 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 22 ~~ \text{and} ~~ r = 6 $. | 4 |
| 2156 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 4 |
| 2157 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 39000 ~~ \text{and} ~~ r = \frac{ 1 }{ 20 } $. | 4 |
| 2158 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 39000 ~~ \text{and} ~~ r = \frac{ 1 }{ 20 } $. | 4 |
| 2159 | Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2160 | Find $ a_10 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 6 $. | 4 |
| 2161 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 64 ~~ \text{and} ~~ r = -\frac{ 3 }{ 2 } $. | 4 |
| 2162 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 4 |
| 2163 | Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $. | 4 |
| 2164 | Find $ a_300 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.015 $. | 4 |
| 2165 | Find $ a_5 $ of a geometric progression if $ a_1 = 512 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 4 |
| 2166 | $$ a_1 = \frac{ 3 }{ 2 } ~,~ r = 2 ~,~ a_n = 1536 ~,~ n = ? $$ | 4 |
| 2167 | Find $ a_2 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $. | 4 |
| 2168 | Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $. | 4 |
| 2169 | $$ a_1 = 100 ~~,~~ r = 0.5 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 4 |
| 2170 | Find $ a_1336 $ of a geometric progression if $ a_1 = 5.2 ~~ \text{and} ~~ r = 1.04 $. | 4 |
| 2171 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 2 } = 6 ~~ \text{and} ~~ a_{ 5 } = 162 $. | 4 |
| 2172 | Find $ a_5 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 4 |
| 2173 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -4 $. | 4 |
| 2174 | Find $ a_4 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 4 |
| 2175 | Find $ a_1 $ of a geometric progression if $ a_1 = 7000 ~~ \text{and} ~~ r = 1.056 $. | 4 |
| 2176 | Find $ a_5 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -4 $. | 4 |
| 2177 | Find $ a_13 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $. | 4 |
| 2178 | Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 4 |
| 2179 | $$ a_1 = 13122 ~,~ r = \frac{ 1 }{ 9 } ~,~ S_n = 1458 ~,~ n = ? $$ | 4 |
| 2180 | Find $ a_24 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 10 $. | 4 |
| 2181 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -2 $. | 4 |
| 2182 | Find $ a_20 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = -2 $. | 4 |
| 2183 | Find $ a_20 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = -5 $. | 4 |
| 2184 | Find $ a_20 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 4 |
| 2185 | Find $ a_20 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 4 |
| 2186 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 4 |
| 2187 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = -7 $. | 4 |
| 2188 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $. | 4 |
| 2189 | Find $ a_3 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $. | 4 |
| 2190 | Find $ a_6 $ of a geometric progression if $ a_1 = 7640 ~~ \text{and} ~~ r = -687.6 $. | 4 |
| 2191 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $. | 4 |
| 2192 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = \frac{ 26 }{ 5 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 4 |
| 2193 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 4 |
| 2194 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 13 ~~ \text{and} ~~ r = \frac{ 1 }{ 12 } $. | 4 |
| 2195 | Find $ a_10 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 4 |
| 2196 | $$ a_1 = \frac{ 1 }{ 81 } ~,~ r = 3 ~,~ S_n = 41 ~,~ n = ? $$ | 4 |
| 2197 | Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -4 $. | 4 |
| 2198 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 3 }{ 4 } ~~ \text{and} ~~ a_{ 3 } = \frac{ 333 }{ 4 } $. | 4 |
| 2199 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 850 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $. | 4 |
| 2200 | Find $ a_30 $ of a geometric progression if $ a_1 = 15000 ~~ \text{and} ~~ r = 1.1 $. | 4 |
