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 $a_{2} 0$ of a geometric progression if $a_{1} = 200 and r = \frac{1}{2}$ .	1
11302	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 10 and a_{7} = 250$ .	1
11303	Find the sum of the first $29$ terms of a geometric sequence if $a_{1} = 16000 and r = 0.92$ .	1
11304	Find $a_{7}$ of a geometric progression if $a_{1} = 27 and r = 6$ .	1
11305	Find $a_{1} 4$ of a geometric progression if $a_{1} = 32 and r = - \frac{1}{4}$ .	1
11306	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 2000 and r = \frac{51}{50}$ .	1
11307	Find $a_{6}$ of a geometric progression if $a_{1} = 729 and r = - \frac{1}{3}$ .	1
11308	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 4 and r = - \frac{1}{2}$ .	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 $a_{1} = 9 and r = - 4$ .	1
11311	Find $a_{4}$ of a geometric progression if $a_{1} = 16 and r = - \frac{1}{2}$ .	1
11312	Find $a_{9}$ of a geometric progression if $a_{1} = - 5 and r = - 1$ .	1
11313	Find $a_{3} 2$ of a geometric progression if $a_{1} = 10000 and r = \frac{1}{2}$ .	1
11314	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{3} = 54 and a_{6} = 1458$ .	1
11315	Find $a_{8}$ of a geometric progression if $a_{1} = 72 and r = - 2$ .	1
11316	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 48 and r = \frac{3}{2}$ .	1
11317	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = 5000 and r = 1.025$ .	1
11318	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = 4000 and r = 1.045$ .	1
11319	Find the sum of the first $1$ terms of a geometric sequence if $a_{1} = \frac{3}{2} and r = 10$ .	1
11320	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = - 3 and r = - \frac{1}{3}$ .	1
11321	Find $a_{5}$ of a geometric progression if $a_{1} = 5 and r = 7$ .	1
11322	Find $a_{9}$ of a geometric progression if $a_{1} = - 32 and r = - \frac{1}{2}$ .	1
11323	Find $a_{5}$ of a geometric progression if $a_{1} = - 8 and r = - \frac{5}{4}$ .	1
11324	Find $a_{4}$ of a geometric progression if $a_{1} = - 11 and r = 6$ .	1
11325	Find $a_{9}$ of a geometric progression if $a_{1} = 3 and r = - 4$ .	1
11326	Find $a_{9}$ of a geometric progression if $a_{1} = - 8 and r = - 2$ .	1
11327	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 18 and r = - 3$ .	1
11328	Find $a_{6}$ of a geometric progression if $a_{1} = 2 and r = - 2$ .	1
11329	$a_{1} = 128, r = \frac{1}{2}, a_{n} = 1, n = ?$	1
11330	Find $a_{1}$ of a geometric progression if $a_{1} = 24 and r = \frac{1}{2}$ .	1
11331	Find $a_{2}$ of a geometric progression if $a_{1} = 24 and r = \frac{1}{2}$ .	1
11332	Find $a_{1} 0$ of a geometric progression if $a_{1} = 72 and r = - \frac{3}{2}$ .	1
11333	Find $a_{7}$ of a geometric progression if $a_{1} = - 4 and r = - 2$ .	1
11334	Find $a_{3}$ of a geometric progression if $a_{1} = 72 and r = \frac{1}{6}$ .	1
11335	Find $a_{5}$ of a geometric progression if $a_{1} = 72 and r = 16$ .	1
11336	Find $a_{6}$ of a geometric progression if $a_{1} = 72 and r = \frac{1}{6}$ .	1
11337	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 9 and r = 5$ .	1
11338	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = - 15 and r = - 2$ .	1
11339	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 12 and r = - 1$ .	1
11340	Find $a_{2}$ of a geometric progression if $a_{1} = - 192 and r = 6$ .	1
11341	Find $a_{2}$ of a geometric progression if $a_{1} = - 192 and r = 4$ .	1
11342	Find $a_{1} 0$ of a geometric progression if $a_{1} = 10 and r = 10$ .	1
11343	Find $a_{1} 0$ of a geometric progression if $a_{1} = 10 and r = 1$ .	1
11344	Find $a_{1}$ of a geometric progression if $a_{1} = 10 and r = 3$ .	1
11345	Find $a_{1}$ of a geometric progression if $a_{1} = 10 and r = - 3$ .	1
11346	Find $a_{1}$ of a geometric progression if $a_{1} = - 3 and r = - 3$ .	1
11347	Find first element ( $a_{1}$ ) of a geometic progression if $r = - 3 and a_{5} = 162$ .	1
11348	Find $a_{3}$ of a geometric progression if $a_{1} = - 118096 and r = 1$ .	1
11349	Find $a_{8}$ of a geometric progression if $a_{1} = 118096 and r = - 3$ .	1
11350	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1 and r = \frac{1}{2}$ .	1