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
3451	Find $ a_1 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 11 } $.	2
3452	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 563500 ~~ \text{and} ~~ r = 1.1 $.	2
3453	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1700000 ~~ \text{and} ~~ r = 1.02 $.	2
3454	Find $ a_5 $ of a geometric progression if $ a_1 = 11 ~~ \text{and} ~~ r = 3 $.	2
3455	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.035 $.	2
3456	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 708588 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	2
3457	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $.	2
3458	$$ a_1 = 6 ~,~ r = 8 ~,~ a_n = 306 ~,~ n = ? $$	2
3459	Find $ a_29 $ of a geometric progression if $ a_1 = 8000 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
3460	Find $ a_10 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = 1.333 $.	2
3461	Find $ a_7 $ of a geometric progression if $ a_1 = 81 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
3462	Find $ a_10 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.	2
3463	Find $ a_9 $ of a geometric progression if $ a_1 = 19 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 10 } $.	2
3464	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 19 ~~ \text{and} ~~ r = 0.9 $.	2
3465	Find $ a_8 $ of a geometric progression if $ a_1 = 320 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
3466	Find $ a_9 $ of a geometric progression if $ a_1 = -10 ~~ \text{and} ~~ r = -5 $.	2
3467	Find $ a_12 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -8 $.	2
3468	Find $ a_6 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -4 $.	2
3469	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 1 } = 5 ~~ \text{and} ~~ a_{ 3 } = 80 $.	2
3470	Find $ a_9 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = 3 $.	2
3471	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 4 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	2
3472	$$ a_1 = 6 ~,~ r = 8 ~,~ a_n = 805306368 ~,~ n = ? $$	2
3473	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 392 ~~ \text{and} ~~ a_{ 4 } = 1687 $.	2
3474	Find $ a_5 $ of a geometric progression if $ a_1 = 392 ~~ \text{and} ~~ r = 1.627 $.	2
3475	Find $ a_8 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 4 $.	2
3476	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -2 $.	2
3477	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
3478	Find $ a_10 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = 1.03 $.	2
3479	Find $ a_5 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -1 $.	2
3480	Find $ a_9 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 14 } $.	2
3481	Find $ a_4 $ of a geometric progression if $ a_1 = -\dfrac{ 5 }{ 2 } ~~ \text{and} ~~ r = 4 $.	2
3482	Find $ a_8 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3483	Find $ a_8 $ of a geometric progression if $ a_1 = 1280 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3484	Find $ a_30 $ of a geometric progression if $ a_1 = 50876 ~~ \text{and} ~~ r = 1.2 $.	2
3485	Find $ a_30 $ of a geometric progression if $ a_1 = 50876 ~~ \text{and} ~~ r = 1.024 $.	2
3486	Find $ a_3 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 12 $.	2
3487	Find $ a_8 $ of a geometric progression if $ a_1 = -10 ~~ \text{and} ~~ r = 2 $.	2
3488	Find $ a_7 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 2 $.	2
3489	Find $ a_6 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
3490	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 10000 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
3491	Find $ a_6 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
3492	Find $ a_8 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 10 } $.	2
3493	Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 3 }{ 4 } ~~ \text{and} ~~ a_{ 3 } = 9 $.	2
3494	Find $ a_5 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 3 $.	2
3495	Find $ a_3 $ of a geometric progression if $ a_1 = 90 ~~ \text{and} ~~ r = 4 $.	2
3496	Find $ a_3 $ of a geometric progression if $ a_1 = 90 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
3497	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 16 } ~~ \text{and} ~~ r = -4 $.	2
3498	Find $ a_7 $ of a geometric progression if $ a_1 = 8.444 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
3499	Find $ a_6 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
3500	Find $ a_6 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2