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
6601	Find $ a_6 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
6602	Find the sum of the first $ 37 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.1 $.	2
6603	Find $ a_16 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.	2
6604	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 1 $.	2
6605	Find $ a_9 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6606	Find $ a_5 $ of a geometric progression if $ a_1 = -135 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
6607	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -\frac{ 3 }{ 7 } $.	2
6608	Find the sum of the first $ 9223372036854775807 $ terms of a geometric sequence if $ a_1 = \frac{ 4 }{ 3 } ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	2
6609	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	2
6610	Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6611	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 320 ~~ \text{and} ~~ a_{ 7 } = 5 $.	2
6612	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
6613	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = 5 $.	2
6614	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 40000 ~~ \text{and} ~~ r = 1.03 $.	2
6615	Find $ a_3 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 4 $.	2
6616	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 10 }{ 11 } $.	2
6617	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 4 } = 192 ~~ \text{and} ~~ a_{ 7 } = 12288 $.	2
6618	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	2
6619	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 10 } $.	2
6620	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 13 }{ 10 } $.	2
6621	Find the sum of the first $ 365 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	2
6622	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 3 ~~ \text{and} ~~ a_{ 3 } = 3 $.	2
6623	Find $ a_8 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
6624	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	2
6625	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 147 ~~ \text{and} ~~ r = 1000 $.	2
6626	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 147 ~~ \text{and} ~~ r = 1000 $.	2
6627	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 147 ~~ \text{and} ~~ r = 1000 $.	2
6628	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 5 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 5 } $.	2
6629	Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ r = 0.7753 $.	2
6630	Find $ a_30 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 2 $.	2
6631	Find $ a_11 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.	2
6632	Find the sum of the first $ 90 $ terms of a geometric sequence if $ a_1 = 5.82 ~~ \text{and} ~~ r = 1.089 $.	2
6633	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
6634	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 43 ~~ \text{and} ~~ r = -3 $.	2
6635	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = 1.031 $.	2
6636	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 1 } = 100 ~~ \text{and} ~~ a_{ 25 } = 220 $.	2
6637	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 60000 ~~ \text{and} ~~ r = 1.035 $.	2
6638	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 12 } = 48 ~~ \text{and} ~~ a_{ 19 } = \frac{ 3 }{ 4 } $.	2
6639	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 2 $.	2
6640	Find $ a_8 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6641	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
6642	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = 4 $.	2
6643	Find $ a_9 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = -4 $.	2
6644	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6645	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
6646	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 39000 ~~ \text{and} ~~ r = 1.025 $.	2
6647	Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = 350 ~~ \text{and} ~~ r = 1.013 $.	2
6648	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 14 ~~ \text{and} ~~ r = \frac{ 1 }{ 25 } $.	2
6649	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 14 ~~ \text{and} ~~ r = \frac{ 1 }{ 100 } $.	2
6650	Find $ a_25 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 10 $.	2