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
9501	Find $ a_2 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
9502	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = \frac{ 9 }{ 10 } $.	1
9503	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 40000 ~~ \text{and} ~~ r = 0.9434 $.	1
9504	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 40000 ~~ \text{and} ~~ r = 0.943 $.	1
9505	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 40000 ~~ \text{and} ~~ r = 0.9159 $.	1
9506	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 40000 ~~ \text{and} ~~ r = 0.9159 $.	1
9507	Find $ a_6 $ of a geometric progression if $ a_1 = -\dfrac{ 49 }{ 2 } ~~ \text{and} ~~ r = -\dfrac{ 6 }{ 7 } $.	1
9508	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $.	1
9509	Find $ a_1 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9510	Find $ a_1 $ of a geometric progression if $ a_1 = 8240 ~~ \text{and} ~~ r = \dfrac{ 21 }{ 20 } $.	1
9511	Find $ a_5 $ of a geometric progression if $ a_1 = 64 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	1
9512	Find the sum of the first $ 39 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 0.9 $.	1
9513	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -1.383 $.	1
9514	Find $ a_144 $ of a geometric progression if $ a_1 = 0.015 ~~ \text{and} ~~ r = 0.015 $.	1
9515	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 0.75 $.	1
9516	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 0.75 $.	1
9517	Find $ a_6 $ of a geometric progression if $ a_1 = 120 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
9518	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 120 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
9519	Find $ a_6 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 5 $.	1
9520	Find $ a_8 $ of a geometric progression if $ a_1 = -9 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
9521	$$ a_1 = 32 ~,~ r = \frac{ 1 }{ 2 } ~,~ a_n = \frac{ 1 }{ 32 } ~,~ n = ? $$	1
9522	Find $ a_12 $ of a geometric progression if $ a_1 = 256 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	1
9523	Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	1
9524	Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = -9 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	1
9525	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 99 }{ 100 } $.	1
9526	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 72 ~~ \text{and} ~~ r = -\frac{ 1 }{ 6 } $.	1
9527	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 360 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
9528	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 3 ~~ \text{and} ~~ a_{ 2 } = -3 $.	1
9529	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
9530	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.4 $.	1
9531	$$ a_1 = \frac{ 1 }{ 64 } ~,~ r = 4 ~,~ S_n = 16 ~,~ n = ? $$	1
9532	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = -\frac{ 1 }{ 5 } $.	1
9533	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 64 ~~ \text{and} ~~ a_{ 4 } = 1 $.	1
9534	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 72 ~~ \text{and} ~~ a_{ 6 } = \frac{ 1 }{ 18 } $.	1
9535	Find $ a_15 $ of a geometric progression if $ a_1 = 0.00023 ~~ \text{and} ~~ r = 1.2 $.	1
9536	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 3 ~~ \text{and} ~~ a_{ 7 } = 1458 $.	1
9537	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 9 }{ 4 } $.	1
9538	Find $ a_2 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 9 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 9 } $.	1
9539	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 9 } ~~ \text{and} ~~ r = \frac{ 1 }{ 9 } $.	1
9540	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
9541	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	1
9542	Find $ a_8 $ of a geometric progression if $ a_1 = 4000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
9543	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
9544	Find $ a_12 $ of a geometric progression if $ a_1 = 1215 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
9545	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -4 $.	1
9546	$$ a_1 = 1 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$	1
9547	Find $ a_1 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9548	Find $ a_4 $ of a geometric progression if $ a_1 = 128 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	1
9549	Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9550	Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 0.071 $.	1