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
6451	Find $ a_15 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 1 $.	2
6452	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 76 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	2
6453	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 81 }{ 2 } ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	2
6454	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 81 }{ 2 } ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	2
6455	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2000 ~~ \text{and} ~~ r = 5 $.	2
6456	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2000 ~~ \text{and} ~~ r = \frac{ 1 }{ 20 } $.	2
6457	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2000 ~~ \text{and} ~~ r = \frac{ 21 }{ 20 } $.	2
6458	Find $ a_5 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = 5 $.	2
6459	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 50 } ~~ \text{and} ~~ r = 5 $.	2
6460	Find $ a_275 $ of a geometric progression if $ a_1 = 11 ~~ \text{and} ~~ r = -55 $.	2
6461	Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
6462	Find $ a_4 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 5 $.	2
6463	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 84 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	2
6464	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6465	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 486 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	2
6466	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	2
6467	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	2
6468	Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	2
6469	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 4 $.	2
6470	Find the sum of the first $ 27 $ terms of a geometric sequence if $ a_1 = 81 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
6471	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	2
6472	Find $ a_9 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
6473	Find $ a_10 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 0.99 $.	2
6474	Find $ a_6 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
6475	Find $ a_10 $ of a geometric progression if $ a_1 = 972 ~~ \text{and} ~~ r = 0.3333 $.	2
6476	Find $ a_10 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = 0.3333 $.	2
6477	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
6478	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 7 $.	2
6479	Find $ a_6 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $.	2
6480	Find $ a_6 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	2
6481	Find $ a_4 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 5 $.	2
6482	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 324 ~~ \text{and} ~~ r = -\frac{ 1 }{ 6 } $.	2
6483	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 6 $.	2
6484	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
6485	Find $ a_5 $ of a geometric progression if $ a_1 = 6144 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6486	Find $ a_12 $ of a geometric progression if $ a_1 = 6144 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6487	Find $ a_14 $ of a geometric progression if $ a_1 = \dfrac{ 7 }{ 24 } ~~ \text{and} ~~ r = -2 $.	2
6488	Find $ a_9 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
6489	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 14 ~~ \text{and} ~~ r = \frac{ 13 }{ 20 } $.	2
6490	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 14 ~~ \text{and} ~~ r = \frac{ 13 }{ 20 } $.	2
6491	Find $ a_7 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 2 $.	2
6492	Find $ a_4 $ of a geometric progression if $ a_1 = 120 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6493	Find $ a_3 $ of a geometric progression if $ a_1 = 1200 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6494	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
6495	Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6496	Find $ a_8 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 250 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
6497	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 3 ~~ \text{and} ~~ a_{ 5 } = 100 $.	2
6498	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 125 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
6499	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 125 } ~~ \text{and} ~~ r = 5 $.	2
6500	Find the sum of the first $ 42 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -1 $.	2