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
1	$$ a_1 = 1 ~,~ r = 5 ~,~ S_n = 3906 ~,~ n = ? $$	675
2	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	108
3	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	62
4	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	60
5	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	55
6	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	53
7	Find $ a_8 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	52
8	Find $ a_9 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	51
9	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	51
10	Find $ a_6 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	51
11	Find $ a_13 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	49
12	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 5 $.	48
13	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	45
14	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	44
15	Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	42
16	Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	40
17	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	40
18	Find $ a_30 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	40
19	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -2 $.	40
20	$$ a_1 = 10 ~,~ r = \frac{ 61 }{ 50 } ~,~ S_n = 360 ~,~ n = ? $$	38
21	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	37
22	Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	37
23	Find $ a_4 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 4 $.	36
24	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	36
25	Find $ a_6 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	35
26	Find $ a_9 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 7 $.	35
27	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	35
28	Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -3 $.	35
29	Find $ a_20 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	34
30	Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $.	34
31	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	34
32	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	34
33	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	34
34	Find $ a_10 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	34
35	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 4 } = \frac{ 4 }{ 3 } ~~ \text{and} ~~ a_{ 8 } = \frac{ 64 }{ 243 } $.	33
36	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	33
37	Find $ a_6 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -4 $.	32
38	Find $ a_6 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	32
39	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	32
40	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	31
41	Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	31
42	Find $ a_9 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -3 $.	30
43	Find $ a_12 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	30
44	Find $ a_9 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -5 $.	30
45	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	30
46	Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	30
47	Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	30
48	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	29
49	Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	29
50	Find $ a_7 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 2 $.	28