Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 2051 | Find $ a_8 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $. | 4 |
| 2052 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 200 ~~ \text{and} ~~ r = 3 $. | 4 |
| 2053 | Find $ a_4 $ of a geometric progression if $ a_1 = 48 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 4 |
| 2054 | Find the sum of the first $ 29 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2055 | Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2056 | Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 4 |
| 2057 | Find the sum of the first $ 9223372036854775807 $ terms of a geometric sequence if $ a_1 = 0.8929 ~~ \text{and} ~~ r = 0.8929 $. | 4 |
| 2058 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 20000 ~~ \text{and} ~~ r = \frac{ 101 }{ 100 } $. | 4 |
| 2059 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 20000 ~~ \text{and} ~~ r = \frac{ 1 }{ 100 } $. | 4 |
| 2060 | Find $ a_8 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -2 $. | 4 |
| 2061 | Find $ a_5 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 4 |
| 2062 | Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 200 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2063 | Find $ a_8 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 4 |
| 2064 | Find $ a_8 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 4 |
| 2065 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 7 }{ 3 } ~~ \text{and} ~~ r = \frac{ 23 }{ 10 } $. | 4 |
| 2066 | Find $ a_5 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 4 |
| 2067 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -4 $. | 4 |
| 2068 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = -3 $. | 4 |
| 2069 | Find $ a_12 $ of a geometric progression if $ a_1 = 25000 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 4 |
| 2070 | $$ a_1 = 25000 ~~,~~ r = \frac{ 9 }{ 5 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 4 |
| 2071 | $$ a_1 = 25000 ~~,~~ r = \frac{ 9 }{ 5 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 4 |
| 2072 | Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -4 $. | 4 |
| 2073 | Find $ a_1095 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2074 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 13 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2075 | Find $ a_11 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 4 |
| 2076 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = 9 $. | 4 |
| 2077 | Find $ a_4 $ of a geometric progression if $ a_1 = -\dfrac{ 5 }{ 4 } ~~ \text{and} ~~ r = -\dfrac{ 4 }{ 7 } $. | 4 |
| 2078 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 4 |
| 2079 | Find $ a_8 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 5 $. | 4 |
| 2080 | Find $ a_11 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 5 $. | 4 |
| 2081 | Find $ a_5 $ of a geometric progression if $ a_1 = -243 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 4 |
| 2082 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2083 | Find the sum of the first $ 29 $ terms of a geometric sequence if $ a_1 = 1830 ~~ \text{and} ~~ r = 1.1 $. | 4 |
| 2084 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -1 $. | 4 |
| 2085 | Find $ a_4 $ of a geometric progression if $ a_1 = 46000 ~~ \text{and} ~~ r = 9 $. | 4 |
| 2086 | Find $ a_4 $ of a geometric progression if $ a_1 = 48000 ~~ \text{and} ~~ r = \dfrac{ 107 }{ 100 } $. | 4 |
| 2087 | $$ a_1 = 3 ~,~ r = 2 ~,~ a_n = 12 ~,~ n = ? $$ | 4 |
| 2088 | $$ a_1 = 6 ~,~ r = \frac{ 3 }{ 5 } ~,~ S_n = \frac{ 63 }{ 16 } ~,~ n = ? $$ | 4 |
| 2089 | Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 10 $. | 4 |
| 2090 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 8 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $. | 4 |
| 2091 | Find $ a_5 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 4 |
| 2092 | Find $ a_6 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = 7 $. | 4 |
| 2093 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $. | 4 |
| 2094 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 4 |
| 2095 | Find $ a_8 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -5 $. | 4 |
| 2096 | Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $. | 4 |
| 2097 | Find $ a_4 $ of a geometric progression if $ a_1 = 1856 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 4 |
| 2098 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 74 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2099 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 10000000 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2100 | Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 4 |
