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
3401	$$ a_1 = \frac{ 37 }{ 1048576 } ~,~ r = 4 ~,~ a_n = 15 ~,~ n = ? $$	2
3402	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 4 ~~ \text{and} ~~ a_{ 12 } = 148 $.	2
3403	$$ a_1 = \frac{ 37 }{ 256 } ~,~ r = 4 ~,~ a_n = 12 ~,~ n = ? $$	2
3404	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
3405	Find $ a_1 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
3406	Find $ a_2 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
3407	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 25 $.	2
3408	Find $ a_3 $ of a geometric progression if $ a_1 = 2.3 ~~ \text{and} ~~ r = 0.26 $.	2
3409	Find $ a_3 $ of a geometric progression if $ a_1 = 2.3 ~~ \text{and} ~~ r = 0.23 $.	2
3410	Find $ a_10 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 4 $.	2
3411	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -\frac{ 3 }{ 2 } ~~ \text{and} ~~ r = -3 $.	2
3412	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
3413	Find $ a_22 $ of a geometric progression if $ a_1 = 25000 ~~ \text{and} ~~ r = 1.1 $.	2
3414	Find $ a_11 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 6 $.	2
3415	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 363600 ~~ \text{and} ~~ r = 1.04 $.	2
3416	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	2
3417	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $.	2
3418	Find $ a_20 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3419	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = 8 $.	2
3420	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
3421	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 1.1 $.	2
3422	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
3423	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 4 ~~ \text{and} ~~ a_{ 5 } = 972 $.	2
3424	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.215 $.	2
3425	Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.215 $.	2
3426	Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.215 $.	2
3427	Find $ a_58 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -3 $.	2
3428	Find $ a_7 $ of a geometric progression if $ a_1 = -4096 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	2
3429	Find the sum of the first $ 26 $ terms of a geometric sequence if $ a_1 = 11000 ~~ \text{and} ~~ r = 1.004 $.	2
3430	Find $ a_3 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = 40 $.	2
3431	Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
3432	Find $ a_5 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
3433	Find $ a_5 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 10 } $.	2
3434	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
3435	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -5 $.	2
3436	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 27 } ~~ \text{and} ~~ r = 3 $.	2
3437	Find $ a_5 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 3 $.	2
3438	Find $ a_9 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 5 $.	2
3439	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = 2 $.	2
3440	Find $ a_6 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	2
3441	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 91 }{ 5 } ~~ \text{and} ~~ r = \frac{ 7 }{ 10 } $.	2
3442	Find $ a_12 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -3 $.	2
3443	Find $ a_10 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	2
3444	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 6 } $.	2
3445	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 1830000 ~~ \text{and} ~~ r = \frac{ 28 }{ 25 } $.	2
3446	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 960000 ~~ \text{and} ~~ r = \frac{ 28 }{ 25 } $.	2
3447	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 960000 ~~ \text{and} ~~ r = \frac{ 28 }{ 25 } $.	2
3448	Find $ a_16 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3449	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
3450	Find $ a_6 $ of a geometric progression if $ a_1 = 28 ~~ \text{and} ~~ r = 4 $.	2