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
10251	$a_{1} = 20, r = \frac{9}{10}, S_{n} = \frac{8853}{20}, n = ?$	1
10252	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = 2 and r = \frac{6}{5}$ .	1
10253	Find the sum of the first $36$ terms of a geometric sequence if $a_{1} = 480 and r = 1.01$ .	1
10254	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{1}{8} and r = 4$ .	1
10255	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 30 and r = - \frac{1}{10}$ .	1
10256	$a_{1} = 1, r = 7, a_{1} = ?, r = ?$	1
10257	$a_{1} = 8, r = 2, a_{n} = 22, n = ?$	1
10258	Find $a_{2} 2$ of a geometric progression if $a_{1} = 8 and r = 2$ .	1
10259	Find $a_{7}$ of a geometric progression if $a_{1} = 1000000000 and r = \frac{1}{10}$ .	1
10260	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 2 and r = - 2$ .	1
10261	Find $a_{7}$ of a geometric progression if $a_{1} = 12 and r = \frac{7}{20}$ .	1
10262	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 32 and r = - \frac{1}{2}$ .	1
10263	Find $a_{2} 0$ of a geometric progression if $a_{1} = 3 and r = 3$ .	1
10264	Find $a_{9}$ of a geometric progression if $a_{1} = 240 and r = \frac{1}{5}$ .	1
10265	Find $a_{2}$ of a geometric progression if $a_{1} = 5 and r = - 2$ .	1
10266	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{5}{4}$ .	1
10267	Find $a_{4}$ of a geometric progression if $a_{1} = 150 and r = 2$ .	1
10268	Find $a_{4}$ of a geometric progression if $a_{1} = 150 and r = 0.5$ .	1
10269	Find $a_{4}$ of a geometric progression if $a_{1} = 150 and r = 1.5$ .	1
10270	Find $a_{9}$ of a geometric progression if $a_{1} = 5 and r = \frac{1}{3}$ .	1
10271	Find $a_{6}$ of a geometric progression if $a_{1} = 8 and r = \frac{2}{3}$ .	1
10272	Find $a_{1}$ of a geometric progression if $a_{1} = 1 and r = \frac{9}{4}$ .	1
10273	Find $a_{9}$ of a geometric progression if $a_{1} = \frac{1}{2} and r = \frac{1}{2}$ .	1
10274	Find $a_{3} 0$ of a geometric progression if $a_{1} = 5000 and r = 1.08$ .	1
10275	Find $a_{5}$ of a geometric progression if $a_{1} = 8 and r = \frac{1}{4}$ .	1
10276	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 5 and r = \frac{3}{4}$ .	1
10277	Find $a_{3} 2$ of a geometric progression if $a_{1} = 9 and r = - 1$ .	1
10278	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1500 and r = 3$ .	1
10279	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = 1512 and r = 6$ .	1
10280	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 12 and r = - 2$ .	1
10281	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = - 12 and r = - 2$ .	1
10282	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = - 4 and r = - 2$ .	1
10283	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 4 and r = - 1$ .	1
10284	Find $a_{9}$ of a geometric progression if $a_{1} = 4 and r = - 1$ .	1
10285	Find first element ( $a_{1}$ ) of a geometic progression if $r = 5 and a_{1} = 3$ .	1
10286	Find first element ( $a_{1}$ ) of a geometic progression if $r = 5 and a_{3} = 3$ .	1
10287	Find $a_{4} 5$ of a geometric progression if $a_{1} = 50000 and r = 0.9808$ .	1
10288	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{8}{5} and r = \frac{9}{10}$ .	1
10289	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = 262144 and r = \frac{1}{8}$ .	1
10290	$a_{1} = \frac{5}{2}, r = 2, a_{n} = 11, n = ?$	1
10291	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{3}{5} and r = \frac{33}{50}$ .	1
10292	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{3}{5} and r = \frac{33}{50}$ .	1
10293	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{1}{4} and r = \frac{1}{4}$ .	1
10294	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 2 and r = - 2$ .	1
10295	Find $a_{7}$ of a geometric progression if $a_{1} = 512 and r = \frac{1}{2}$ .	1
10296	Find $a_{3}$ of a geometric progression if $a_{1} = 50 and r = 80$ .	1
10297	Find $a_{5} 0$ of a geometric progression if $a_{1} = 80 and r = 3$ .	1
10298	Find $a_{5} 0$ of a geometric progression if $a_{1} = 3 and r = 90$ .	1
10299	Find $a_{1} 0$ of a geometric progression if $a_{1} = 2 and r = 15$ .	1
10300	Find $a_{2}$ of a geometric progression if $a_{1} = 15 and r = 10$ .	1