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
3501	Find $ a_6 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 10 } $.	2
3502	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -20 ~~ \text{and} ~~ r = -2 $.	2
3503	Find $ a_3 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $.	2
3504	Find $ a_6 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	2
3505	$$ a_1 = -1 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
3506	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 2 ~~ \text{and} ~~ a_{ 5 } = 152 $.	2
3507	Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -8 $.	2
3508	Find $ a_12 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 3 $.	2
3509	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -\frac{ 2 }{ 3 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	2
3510	Find $ a_3 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3511	$$ a_1 = 1 ~,~ r = 3 ~,~ S_n = 1093 ~,~ n = ? $$	2
3512	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 14 ~~ \text{and} ~~ r = 5 $.	2
3513	$$ a_1 = 4 ~,~ r = 4 ~,~ S_n = 820 ~,~ n = ? $$	2
3514	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	2
3515	$$ a_1 = 729 ~,~ r = 3 ~,~ a_n = 1 ~,~ n = ? $$	2
3516	$$ a_1 = 729 ~,~ r = \frac{ 1 }{ 3 } ~,~ a_n = 1 ~,~ n = ? $$	2
3517	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	2
3518	Find $ a_64 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -8 $.	2
3519	Find $ a_11 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
3520	Find $ a_4 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = 12 $.	2
3521	Find $ a_8 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 4 $.	2
3522	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
3523	$$ a_1 = 5 ~,~ r = 3 ~,~ a_n = 10935 ~,~ n = ? $$	2
3524	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 3645 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	2
3525	Find $ a_6 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = 3 $.	2
3526	Find $ a_6 $ of a geometric progression if $ a_1 = -192 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	2
3527	Find $ a_6 $ of a geometric progression if $ a_1 = 224 ~~ \text{and} ~~ r = 0.5 $.	2
3528	Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 2 }{ 5 } ~~ \text{and} ~~ a_{ 8 } = \frac{ 1 }{ 125 } $.	2
3529	Find $ a_2 $ of a geometric progression if $ a_1 = 128 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3530	Find $ a_5 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -\dfrac{ 5 }{ 2 } $.	2
3531	Find $ a_8 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -6 $.	2
3532	Find $ a_12 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $.	2
3533	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	2
3534	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 5 }{ 6 } $.	2
3535	Find $ a_10 $ of a geometric progression if $ a_1 = 5000 ~~ \text{and} ~~ r = 2 $.	2
3536	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 4 }{ 5 } ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	2
3537	$$ a_1 = 6 ~,~ r = 7 ~,~ a_n = 1296 ~,~ n = ? $$	2
3538	$$ a_1 = 10 ~~,~~ r = \frac{ 1 }{ 2 } ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
3539	Find $ a_3 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	2
3540	Find $ a_3 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 5 $.	2
3541	Find the sum of the first $ 22 $ terms of a geometric sequence if $ a_1 = 31500 ~~ \text{and} ~~ r = 0.94 $.	2
3542	Find $ a_9 $ of a geometric progression if $ a_1 = 249500 ~~ \text{and} ~~ r = 1.24 $.	2
3543	Find $ a_4 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3544	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 5 }{ 3 } $.	2
3545	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 16807 ~~ \text{and} ~~ r = -7 $.	2
3546	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 3000 ~~ \text{and} ~~ r = 1.05 $.	2
3547	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -0.3 $.	2
3548	Find the sum of the first $ 22 $ terms of a geometric sequence if $ a_1 = -10 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
3549	Find $ a_4 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3550	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2