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
5601	Find $ a_100 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.015 $.	2
5602	Find $ a_200 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.015 $.	2
5603	Find $ a_400 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.015 $.	2
5604	Find $ a_200 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.02 $.	2
5605	Find $ a_300 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.02 $.	2
5606	Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	2
5607	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 7 ~~ \text{and} ~~ a_{ 3 } = \frac{ 7 }{ 20 } $.	2
5608	Find $ a_500 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 1 $.	2
5609	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 125 } ~~ \text{and} ~~ r = 5 $.	2
5610	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 125 } ~~ \text{and} ~~ r = 5 $.	2
5611	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 12 ~~ \text{and} ~~ a_{ 3 } = 48 $.	2
5612	Find $ a_1 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 1.035 $.	2
5613	Find $ a_2 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 1.035 $.	2
5614	Find $ a_6 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 9 $.	2
5615	Find $ a_2 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 20 } $.	2
5616	Find $ a_24 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	2
5617	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -3 $.	2
5618	Find $ a_1 $ of a geometric progression if $ a_1 = 5000 ~~ \text{and} ~~ r = \dfrac{ 69 }{ 50 } $.	2
5619	Find $ a_7 $ of a geometric progression if $ a_1 = 8192 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5620	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = 4 $.	2
5621	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = 6 $.	2
5622	Find $ a_1 $ of a geometric progression if $ a_1 = 8243 ~~ \text{and} ~~ r = 1.056 $.	2
5623	Find $ a_2 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -2 $.	2
5624	Find the sum of the first $ 35 $ terms of a geometric sequence if $ a_1 = 21 ~~ \text{and} ~~ r = 3 $.	2
5625	Find the sum of the first $ 35 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	2
5626	Find $ a_8 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 3 $.	2
5627	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = 3 $.	2
5628	Find $ a_4 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5629	Find $ a_11 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = -2 $.	2
5630	Find $ a_11 $ of a geometric progression if $ a_1 = 2.786 ~~ \text{and} ~~ r = 10 $.	2
5631	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	2
5632	Find $ a_15 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 19 } $.	2
5633	Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $.	2
5634	Find $ a_3 $ of a geometric progression if $ a_1 = 1780 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5635	Find $ a_6 $ of a geometric progression if $ a_1 = 25000 ~~ \text{and} ~~ r = 0.00032 $.	2
5636	Find $ a_5 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = -4 $.	2
5637	$$ a_1 = 25 ~,~ r = 3 ~,~ a_n = 4 ~,~ n = ? $$	2
5638	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 200 ~~ \text{and} ~~ r = -\frac{ 4 }{ 5 } $.	2
5639	$$ a_1 = 7 ~,~ r = \frac{ 9 }{ 19 } ~,~ a_n = 9 ~,~ n = ? $$	2
5640	Find $ a_7 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	2
5641	Find $ a_10 $ of a geometric progression if $ a_1 = 1536 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5642	Find $ a_7 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 1 $.	2
5643	Find $ a_7 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 4 $.	2
5644	Find $ a_6 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 7 $.	2
5645	Find $ a_1 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	2
5646	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5647	$$ a_1 = 4 ~,~ r = 3 ~,~ S_n = 160 ~,~ n = ? $$	2
5648	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 20000 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5649	Find the sum of the first $ 500 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.2 $.	2
5650	$$ a_1 = 0.1 ~,~ r = 2 ~,~ S_n = 100 ~,~ n = ? $$	2