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
11301	Find $ a_20 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
11302	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 10 ~~ \text{and} ~~ a_{ 7 } = 250 $.	1
11303	Find the sum of the first $ 29 $ terms of a geometric sequence if $ a_1 = 16000 ~~ \text{and} ~~ r = 0.92 $.	1
11304	Find $ a_7 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = 6 $.	1
11305	Find $ a_14 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	1
11306	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 2000 ~~ \text{and} ~~ r = \frac{ 51 }{ 50 } $.	1
11307	Find $ a_6 $ of a geometric progression if $ a_1 = 729 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	1
11308	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
11309	$$ a_1 = 2 ~,~ r = 4 ~,~ S_n = 21 ~,~ n = ? $$	1
11310	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = -4 $.	1
11311	Find $ a_4 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
11312	Find $ a_9 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -1 $.	1
11313	Find $ a_32 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
11314	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 54 ~~ \text{and} ~~ a_{ 6 } = 1458 $.	1
11315	Find $ a_8 $ of a geometric progression if $ a_1 = 72 ~~ \text{and} ~~ r = -2 $.	1
11316	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 48 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
11317	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 5000 ~~ \text{and} ~~ r = 1.025 $.	1
11318	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 4000 ~~ \text{and} ~~ r = 1.045 $.	1
11319	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ r = 10 $.	1
11320	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	1
11321	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 7 $.	1
11322	Find $ a_9 $ of a geometric progression if $ a_1 = -32 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
11323	Find $ a_5 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -\dfrac{ 5 }{ 4 } $.	1
11324	Find $ a_4 $ of a geometric progression if $ a_1 = -11 ~~ \text{and} ~~ r = 6 $.	1
11325	Find $ a_9 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -4 $.	1
11326	Find $ a_9 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -2 $.	1
11327	Find $ a_10 $ of a geometric progression if $ a_1 = -18 ~~ \text{and} ~~ r = -3 $.	1
11328	Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -2 $.	1
11329	$$ a_1 = 128 ~,~ r = \frac{ 1 }{ 2 } ~,~ a_n = 1 ~,~ n = ? $$	1
11330	Find $ a_1 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
11331	Find $ a_2 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
11332	Find $ a_10 $ of a geometric progression if $ a_1 = 72 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 2 } $.	1
11333	Find $ a_7 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -2 $.	1
11334	Find $ a_3 $ of a geometric progression if $ a_1 = 72 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 6 } $.	1
11335	Find $ a_5 $ of a geometric progression if $ a_1 = 72 ~~ \text{and} ~~ r = 16 $.	1
11336	Find $ a_6 $ of a geometric progression if $ a_1 = 72 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 6 } $.	1
11337	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = 5 $.	1
11338	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -15 ~~ \text{and} ~~ r = -2 $.	1
11339	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = -1 $.	1
11340	Find $ a_2 $ of a geometric progression if $ a_1 = -192 ~~ \text{and} ~~ r = 6 $.	1
11341	Find $ a_2 $ of a geometric progression if $ a_1 = -192 ~~ \text{and} ~~ r = 4 $.	1
11342	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 10 $.	1
11343	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1 $.	1
11344	Find $ a_1 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 3 $.	1
11345	Find $ a_1 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -3 $.	1
11346	Find $ a_1 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -3 $.	1
11347	Find first element ( $ a_1 $ ) of a geometic progression if $ r = -3 ~~ \text{and} ~~ a_{ 5 } = 162 $.	1
11348	Find $ a_3 $ of a geometric progression if $ a_1 = -118096 ~~ \text{and} ~~ r = 1 $.	1
11349	Find $ a_8 $ of a geometric progression if $ a_1 = 118096 ~~ \text{and} ~~ r = -3 $.	1
11350	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1