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	$a_{1} = 1, r = 5, S_{n} = 3906, n = ?$	530
2	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 3 and r = 2$ .	85
3	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1 and r = 2$ .	49
4	Find $a_{5}$ of a geometric progression if $a_{1} = 2 and r = 3$ .	48
5	Find $a_{5}$ of a geometric progression if $a_{1} = 3 and r = 2$ .	47
6	Find $a_{6}$ of a geometric progression if $a_{1} = 5 and r = \frac{3}{2}$ .	46
7	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1 and r = 2$ .	46
8	Find $a_{8}$ of a geometric progression if $a_{1} = 6 and r = - \frac{1}{3}$ .	45
9	Find $a_{1} 3$ of a geometric progression if $a_{1} = 3 and r = 2$ .	45
10	Find $a_{5}$ of a geometric progression if $a_{1} = 1 and r = 2$ .	43
11	Find $a_{9}$ of a geometric progression if $a_{1} = 1 and r = - \frac{1}{3}$ .	42
12	Find $a_{1} 0$ of a geometric progression if $a_{1} = 3 and r = 5$ .	41
13	Find $a_{5}$ of a geometric progression if $a_{1} = 4 and r = 3$ .	40
14	Find $a_{1} 0$ of a geometric progression if $a_{1} = 2 and r = 2$ .	40
15	$a_{1} = 10, r = \frac{61}{50}, S_{n} = 360, n = ?$	38
16	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1 and r = 2$ .	36
17	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = 1 and r = 2$ .	36
18	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 2 and r = 3$ .	35
19	Find $a_{2} 0$ of a geometric progression if $a_{1} = 2 and r = 3$ .	34
20	Find $a_{9}$ of a geometric progression if $a_{1} = - 1 and r = 7$ .	34
21	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 1 and r = 2$ .	34
22	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 2 and r = 2$ .	33
23	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 4 and r = 3$ .	33
24	Find $a_{8}$ of a geometric progression if $a_{1} = 2 and r = 4$ .	33
25	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 5 and r = 2$ .	33
26	Find $a_{1} 0$ of a geometric progression if $a_{1} = 10 and r = - 2$ .	33
27	Find $a_{8}$ of a geometric progression if $a_{1} = 4 and r = - 3$ .	31
28	Find $a_{4}$ of a geometric progression if $a_{1} = 8 and r = 4$ .	31
29	Find $a_{7}$ of a geometric progression if $a_{1} = 1 and r = - 3$ .	31
30	Find $a_{1} 0$ of a geometric progression if $a_{1} = 3 and r = 2$ .	30
31	Find $a_{1} 0$ of a geometric progression if $a_{1} = 4 and r = \frac{1}{2}$ .	30
32	Find $a_{5}$ of a geometric progression if $a_{1} = 1 and r = 3$ .	29
33	Find $a_{9}$ of a geometric progression if $a_{1} = 6 and r = - 3$ .	29
34	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 3 and r = - 4$ .	28
35	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{4} = \frac{4}{3} and a_{8} = \frac{64}{243}$ .	28
36	Find $a_{7}$ of a geometric progression if $a_{1} = 4 and r = 3$ .	28
37	Find $a_{8}$ of a geometric progression if $a_{1} = 2 and r = 2$ .	27
38	Find $a_{3} 0$ of a geometric progression if $a_{1} = 1 and r = 2$ .	27
39	Find $a_{1} 2$ of a geometric progression if $a_{1} = 1 and r = 3$ .	27
40	Find $a_{9}$ of a geometric progression if $a_{1} = - 2 and r = - 5$ .	27
41	Find $a_{6}$ of a geometric progression if $a_{1} = 5 and r = 2$ .	27
42	Find $a_{7}$ of a geometric progression if $a_{1} = 1 and r = - \frac{2}{3}$ .	27
43	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = 10 and r = 1.22$ .	27
44	Find $a_{8}$ of a geometric progression if $a_{1} = 3 and r = 2$ .	26
45	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 2 and r = 3$ .	26
46	Find $a_{6}$ of a geometric progression if $a_{1} = 5 and r = 3$ .	26
47	Find $a_{5}$ of a geometric progression if $a_{1} = 5 and r = 3$ .	26
48	Find $a_{1} 2$ of a geometric progression if $a_{1} = 1 and r = 2$ .	26
49	Find $a_{1} 4$ of a geometric progression if $a_{1} = 10 and r = 2$ .	25
50	Find $a_{6}$ of a geometric progression if $a_{1} = - 2 and r = - 5$ .	25