Geometric sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Geometric sequences.

Select category

ID	Problem	Count
4501	$$ a_1 = 7 ~,~ r = 2 ~,~ a_n = 7168 ~,~ n = ? $$	2
4502	Find $ a_7 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 3 $.	2
4503	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 140 ~~ \text{and} ~~ r = -\frac{ 3 }{ 4 } $.	2
4504	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
4505	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	2
4506	Find $ a_10 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = 2.5 $.	2
4507	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	2
4508	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 27 }{ 4 } ~~ \text{and} ~~ r = 3 $.	2
4509	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 7 }{ 2 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 7 } $.	2
4510	Find $ a_3 $ of a geometric progression if $ a_1 = 1000000 ~~ \text{and} ~~ r = 1.065 $.	2
4511	Find $ a_7 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = 6 $.	2
4512	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 2 } ~~ \text{and} ~~ r = 4 $.	2
4513	Find the sum of the first $ 74 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 5 }{ 6 } $.	2
4514	Find $ a_8 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 3 $.	2
4515	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	2
4516	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 25000 ~~ \text{and} ~~ r = 0.025 $.	2
4517	Find $ a_40 $ of a geometric progression if $ a_1 = 1458 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
4518	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 6 } = 224 ~~ \text{and} ~~ a_{ 1 } = 7 $.	2
4519	Find $ a_5 $ of a geometric progression if $ a_1 = 115 ~~ \text{and} ~~ r = \dfrac{ 13 }{ 20 } $.	2
4520	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 37 } = 48000 ~~ \text{and} ~~ a_{ 1 } = 500 $.	2
4521	Find $ a_20 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4522	Find $ a_8 $ of a geometric progression if $ a_1 = 12000 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.	2
4523	Find $ a_8 $ of a geometric progression if $ a_1 = 12000 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.	2
4524	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 50 } ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $.	2
4525	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	2
4526	Find $ a_10 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
4527	Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 5 }{ 4 } ~~ \text{and} ~~ a_{ 4 } = 12 $.	2
4528	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	2
4529	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 120 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	2
4530	Find $ a_10 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -4 $.	2
4531	Find $ a_1 $ of a geometric progression if $ a_1 = 3280 ~~ \text{and} ~~ r = 3 $.	2
4532	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 20000 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	2
4533	$$ a_1 = 3280 ~,~ r = 3 ~,~ a_n = 8 ~,~ n = ? $$	2
4534	Find $ a_5 $ of a geometric progression if $ a_1 = 0.75 ~~ \text{and} ~~ r = 4 $.	2
4535	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 4 }{ 5 } ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $.	2
4536	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 2 }{ 25 } ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $.	2
4537	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 5 } ~~ \text{and} ~~ r = 3 $.	2
4538	Find $ a_10 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 2 $.	2
4539	$$ a_1 = 2 ~,~ r = 2 ~,~ a_n = 128 ~,~ n = ? $$	2
4540	Find $ a_2 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 5 $.	2
4541	$$ a_1 = 20 ~,~ r = 2 ~,~ S_n = 40940 ~,~ n = ? $$	2
4542	Find $ a_11 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -3 $.	2
4543	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 417 ~~ \text{and} ~~ a_{ 5 } = 71400 $.	2
4544	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 417 ~~ \text{and} ~~ a_{ 56 } = 71400 $.	2
4545	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 1 } = 417 ~~ \text{and} ~~ a_{ 56 } = 71400 $.	2
4546	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 100 } ~~ \text{and} ~~ r = 2 $.	2
4547	Find $ a_9 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -4 $.	2
4548	Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 91000 ~~ \text{and} ~~ r = \frac{ 103 }{ 100 } $.	2
4549	Find the sum of the first $ 28 $ terms of a geometric sequence if $ a_1 = 30 ~~ \text{and} ~~ r = 0.91 $.	2
4550	Find $ a_4 $ of a geometric progression if $ a_1 = 424600 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	2