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
9601	Find $ a_15 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	1
9602	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
9603	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -3 $.	1
9604	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 10 } ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	1
9605	Find $ a_4 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -5 $.	1
9606	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
9607	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
9608	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 7 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
9609	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 27 }{ 2 } ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
9610	Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = 1.8 $.	1
9611	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	1
9612	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.1 $.	1
9613	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.1 $.	1
9614	Find $ a_15 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	1
9615	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 6 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
9616	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = 2 $.	1
9617	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 6 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
9618	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
9619	Find $ a_9 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -3 $.	1
9620	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 0.75 $.	1
9621	Find $ a_4 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 0.75 $.	1
9622	Find $ a_12 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	1
9623	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 3 ~~ \text{and} ~~ a_{ 5 } = 24 $.	1
9624	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	1
9625	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	1
9626	$$ a_1 = 10 ~,~ r = 2 ~,~ S_n = 20 ~,~ n = ? $$	1
9627	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 49 }{ 2 } ~~ \text{and} ~~ r = 3 $.	1
9628	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ r = 10 $.	1
9629	Find $ a_2 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 2 $.	1
9630	Find $ a_5 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 2 $.	1
9631	Find $ a_12 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 2 $.	1
9632	Find $ a_24 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 2 $.	1
9633	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $.	1
9634	Find $ a_12 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -3 $.	1
9635	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 400 ~~ \text{and} ~~ r = 200 $.	1
9636	Find $ a_12 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -2 $.	1
9637	Find $ a_10 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -\dfrac{ 7 }{ 2 } $.	1
9638	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 21 }{ 10 } $.	1
9639	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 21 }{ 10 } $.	1
9640	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -\frac{ 7 }{ 2 } $.	1
9641	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 32 ~~ \text{and} ~~ a_{ 5 } = 2 $.	1
9642	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = 1.42 $.	1
9643	Find $ a_6 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
9644	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 16000000 ~~ \text{and} ~~ r = 2 $.	1
9645	Find $ a_8 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -3 $.	1
9646	Find $ a_9 $ of a geometric progression if $ a_1 = 0.5 ~~ \text{and} ~~ r = -2 $.	1
9647	Find $ a_9 $ of a geometric progression if $ a_1 = -14 ~~ \text{and} ~~ r = 3 $.	1
9648	Find $ a_7 $ of a geometric progression if $ a_1 = -14 ~~ \text{and} ~~ r = -3 $.	1
9649	Find $ a_7 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = -1 $.	1
9650	Find $ a_11 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = 2 $.	1