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
10151	Find $a_{4}$ of a geometric progression if $a_{1} = 128 and r = \frac{1}{2}$ .	1
10152	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{2}{3} and r = - \frac{1}{3}$ .	1
10153	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 64 and r = - 0.75$ .	1
10154	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 0 and r = 2$ .	1
10155	Find $a_{5}$ of a geometric progression if $a_{1} = 10000 and r = \frac{4}{5}$ .	1
10156	Find first element ( $a_{1}$ ) of a geometic progression if $r = 5 and a_{6} = 15$ .	1
10157	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 100 and r = \frac{1}{10}$ .	1
10158	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{3}{5} and r = \frac{1}{3}$ .	1
10159	Find $a_{1} 1$ of a geometric progression if $a_{1} = - 1 and r = - 7$ .	1
10160	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 60000 and r = \frac{23}{20}$ .	1
10161	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 20 and r = \frac{26}{27}$ .	1
10162	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 500 and r = \frac{2}{3}$ .	1
10163	Find $a_{1} 0$ of a geometric progression if $a_{1} = 500 and r = \frac{2}{3}$ .	1
10164	Find the sum of the first $1000$ terms of a geometric sequence if $a_{1} = \frac{1}{2} and r = \frac{1}{2}$ .	1
10165	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{1}{2} and r = \frac{1}{2}$ .	1
10166	Find the sum of the first $480$ terms of a geometric sequence if $a_{1} = 500 and r = 1.006$ .	1
10167	Find the sum of the first $480$ terms of a geometric sequence if $a_{1} = 500 and r = 1.006$ .	1
10168	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{5}{343} and r = 7$ .	1
10169	Find $a_{2}$ of a geometric progression if $a_{1} = 3 and r = - 2$ .	1
10170	Find $a_{1} 0$ of a geometric progression if $a_{1} = 64 and r = - \frac{1}{4}$ .	1
10171	$a_{1} = 6, r = 2, a_{n} = 8, n = ?$	1
10172	Find $a_{6} 0$ of a geometric progression if $a_{1} = 100 and r = 1.005$ .	1
10173	Find $a_{2}$ of a geometric progression if $a_{1} = 50 and r = 25$ .	1
10174	Find the sum of the first $360$ terms of a geometric sequence if $a_{1} = 51 and r = 1.02$ .	1
10175	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 7 and r = 1$ .	1
10176	$a_{1} = 1133, r = 0.00967, S_{n} = 37890, n = ?$	1
10177	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 1500 and r = 2$ .	1
10178	Find $a_{2}$ of a geometric progression if $a_{1} = 1000 and r = 2$ .	1
10179	Find $a_{2} 0$ of a geometric progression if $a_{1} = 1000 and r = 2$ .	1
10180	Find $a_{1} 6$ of a geometric progression if $a_{1} = 1000 and r = 2$ .	1
10181	Find $a_{4}$ of a geometric progression if $a_{1} = - 3 and r = - 3$ .	1
10182	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{9}{5}$ .	1
10183	Find $a_{8}$ of a geometric progression if $a_{1} = 4 and r = 3$ .	1
10184	Find $a_{7}$ of a geometric progression if $a_{1} = 3 and r = 3$ .	1
10185	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 3 and r = 3$ .	1
10186	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 4 and r = 3$ .	1
10187	Find $a_{8}$ of a geometric progression if $a_{1} = 18 and r = 1.66$ .	1
10188	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{3}{16} and r = \frac{27}{64}$ .	1
10189	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = - 2 and r = - 4$ .	1
10190	Find $a_{1} 4$ of a geometric progression if $a_{1} = 6 and r = - 3$ .	1
10191	Find $a_{7}$ of a geometric progression if $a_{1} = 18 and r = - 3$ .	1
10192	Find $a_{6}$ of a geometric progression if $a_{1} = 400 and r = \frac{1}{5}$ .	1
10193	Find the sum of the first $36$ terms of a geometric sequence if $a_{1} = 1 and r = 1.005$ .	1
10194	Find the sum of the first $36$ terms of a geometric sequence if $a_{1} = 36 and r = 1.005$ .	1
10195	Find $a_{5}$ of a geometric progression if $a_{1} = 0 and r = - 4$ .	1
10196	Find $a_{2}$ of a geometric progression if $a_{1} = - \frac{1}{100} and r = - 10$ .	1
10197	Find $a_{7}$ of a geometric progression if $a_{1} = 625 and r = \frac{1}{5}$ .	1
10198	Find first element ( $a_{1}$ ) of a geometic progression if $r = - 2 and a_{8} = 124$ .	1
10199	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{7}{4} and r = \frac{7}{4}$ .	1
10200	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 0 and r = - \frac{1}{3}$ .	1