Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 1201 | Find $ a_6 $ of a geometric progression if $ a_1 = 96 ~~ \text{and} ~~ r = 3 $. | 5 |
| 1202 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = 4 ~~ \text{and} ~~ a_{ 12 } = 100663296 $. | 5 |
| 1203 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 33 }{ 50 } $. | 5 |
| 1204 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 5 |
| 1205 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 7300 ~~ \text{and} ~~ r = 1.7 $. | 5 |
| 1206 | Find $ a_10 $ of a geometric progression if $ a_1 = 512 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 5 |
| 1207 | $$ a_1 = 1 ~,~ r = 2 ~,~ a_n = 32 ~,~ n = ? $$ | 5 |
| 1208 | Find $ a_36 $ of a geometric progression if $ a_1 = 40000 ~~ \text{and} ~~ r = 1.1 $. | 5 |
| 1209 | Find $ a_33 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $. | 5 |
| 1210 | Find the sum of the first $ 33 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $. | 5 |
| 1211 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -5 ~~ \text{and} ~~ r = -2 $. | 5 |
| 1212 | Find $ a_8 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -3 $. | 5 |
| 1213 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = -2 $. | 5 |
| 1214 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $. | 5 |
| 1215 | Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = 2 $. | 5 |
| 1216 | Find $ a_4 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = 2 $. | 5 |
| 1217 | Find $ a_4 $ of a geometric progression if $ a_1 = 46000 ~~ \text{and} ~~ r = \dfrac{ 109 }{ 100 } $. | 5 |
| 1218 | Find $ a_5 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $. | 5 |
| 1219 | Find $ a_15 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = 2 $. | 5 |
| 1220 | Find $ a_8 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 6 $. | 5 |
| 1221 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 5 |
| 1222 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $. | 5 |
| 1223 | Find $ a_10 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -2 $. | 5 |
| 1224 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 72 }{ 7 } ~~ \text{and} ~~ a_{ 2 } = \frac{ 576 }{ 49 } $. | 5 |
| 1225 | Find $ a_10 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -2 $. | 5 |
| 1226 | $$ a_1 = 12 ~,~ r = \frac{ 11 }{ 10 } ~,~ S_n = 100 ~,~ n = ? $$ | 5 |
| 1227 | Find $ a_11 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 5 $. | 5 |
| 1228 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 5 |
| 1229 | Find $ a_9 $ of a geometric progression if $ a_1 = 17 ~~ \text{and} ~~ r = 34 $. | 5 |
| 1230 | Find $ a_5 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 5 |
| 1231 | $$ a_1 = 50 ~,~ r = \frac{ 1 }{ 5 } ~,~ a_n = 5 ~,~ n = ? $$ | 5 |
| 1232 | $$ a_1 = 5 ~,~ r = 160 ~,~ a_n = 6 ~,~ n = ? $$ | 5 |
| 1233 | Find $ a_2 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $. | 5 |
| 1234 | Find $ a_6 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 5 |
| 1235 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -6 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 5 |
| 1236 | Find $ a_6 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -3 $. | 5 |
| 1237 | Find $ a_1 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 2 $. | 5 |
| 1238 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -3 $. | 5 |
| 1239 | Find $ a_5 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 0.8 $. | 5 |
| 1240 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -3 $. | 5 |
| 1241 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 5 |
| 1242 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 5 }{ 7 } $. | 5 |
| 1243 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 15 } = 29 ~~ \text{and} ~~ a_{ 33 } = 101 $. | 5 |
| 1244 | Find $ a_18 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $. | 5 |
| 1245 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = -5 $. | 5 |
| 1246 | Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 0.01 ~~ \text{and} ~~ r = 2 $. | 5 |
| 1247 | Find $ a_5 $ of a geometric progression if $ a_1 = 0.0124 ~~ \text{and} ~~ r = 100 $. | 5 |
| 1248 | Find $ a_5 $ of a geometric progression if $ a_1 = 250 ~~ \text{and} ~~ r = \dfrac{ 107 }{ 100 } $. | 5 |
| 1249 | Find $ a_5 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = 2 $. | 5 |
| 1250 | Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $. | 5 |
