Geometric sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Geometric sequences.

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ID	Problem	Count
2201	Find $ a_20 $ of a geometric progression if $ a_1 = 25000 ~~ \text{and} ~~ r = 1.1 $.	4
2202	Find $ a_23 $ of a geometric progression if $ a_1 = 25000 ~~ \text{and} ~~ r = 1.1 $.	4
2203	Find $ a_24 $ of a geometric progression if $ a_1 = 25000 ~~ \text{and} ~~ r = 1.1 $.	4
2204	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 2500 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	4
2205	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 700000 ~~ \text{and} ~~ r = \frac{ 17 }{ 20 } $.	4
2206	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 850 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $.	4
2207	Find $ a_6 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = 2 $.	4
2208	Find $ a_5 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	4
2209	Find $ a_3 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	4
2210	Find $ a_24 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $.	4
2211	Find $ a_12 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -4 $.	4
2212	Find $ a_16 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 2 $.	4
2213	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 14 $.	4
2214	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 9 }{ 2 } ~~ \text{and} ~~ r = 2 $.	4
2215	Find $ a_10 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = 3 $.	4
2216	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 21000 ~~ \text{and} ~~ r = \frac{ 26 }{ 25 } $.	4
2217	Find $ a_10 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	4
2218	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	4
2219	$$ a_1 = 4 ~,~ r = 2 ~,~ a_n = 4 ~,~ n = ? $$	4
2220	Find $ a_9 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	4
2221	Find $ a_5 $ of a geometric progression if $ a_1 = -375 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	4
2222	Find $ a_5 $ of a geometric progression if $ a_1 = 23000 ~~ \text{and} ~~ r = \dfrac{ 103 }{ 100 } $.	4
2223	Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	4
2224	Find $ a_12 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -4 $.	4
2225	Find $ a_6 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	4
2226	Find $ a_7 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	4
2227	Find $ a_10 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	4
2228	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 5 }{ 32 } $.	4
2229	Find $ a_7 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 32 } $.	4
2230	Find $ a_6 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 32 } $.	4
2231	Find $ a_36 $ of a geometric progression if $ a_1 = 0.9972 ~~ \text{and} ~~ r = 0.9972 $.	4
2232	$$ a_1 = 1 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$	4
2233	Find $ a_9 $ of a geometric progression if $ a_1 = -78125 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	4
2234	Find $ a_2 $ of a geometric progression if $ a_1 = 150 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $.	4
2235	Find $ a_9 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	4
2236	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -2 $.	4
2237	Find the sum of the first $ 252 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = 1.003 $.	4
2238	Find $ a_9 $ of a geometric progression if $ a_1 = -20 ~~ \text{and} ~~ r = -2 $.	4
2239	Find $ a_3 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	4
2240	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -2 $.	4
2241	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	4
2242	Find $ a_9 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $.	4
2243	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = \frac{ 15 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	4
2244	Find $ a_11 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	4
2245	Find the sum of the first $ 19 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	4
2246	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 4 } ~~ \text{and} ~~ r = 2 $.	4
2247	Find $ a_8 $ of a geometric progression if $ a_1 = 2700 ~~ \text{and} ~~ r = 10 $.	4
2248	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 26 ~~ \text{and} ~~ r = 5 $.	4
2249	Find $ a_1 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = 2 $.	4
2250	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	4