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
11251	Find $a_{1} 7$ of a geometric progression if $a_{1} = 1 and r = 9$ .	1
11252	Find $a_{1} 7$ of a geometric progression if $a_{1} = 6 and r = - 3$ .	1
11253	Find $a_{6}$ of a geometric progression if $a_{1} = 15 and r = \frac{2}{3}$ .	1
11254	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{49}{8} and r = \frac{7}{8}$ .	1
11255	Find $a_{1} 9$ of a geometric progression if $a_{1} = - 3 and r = - 2$ .	1
11256	Find $a_{1} 3$ of a geometric progression if $a_{1} = - 3 and r = - 2$ .	1
11257	Find $a_{5}$ of a geometric progression if $a_{1} = 48 and r = - \frac{1}{2}$ .	1
11258	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = - 2 and r = 3$ .	1
11259	Find $a_{7}$ of a geometric progression if $a_{1} = 250 and r = \frac{4}{5}$ .	1
11260	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 3 and r = 7$ .	1
11261	Find $a_{1} 2$ of a geometric progression if $a_{1} = 11 and r = 4$ .	1
11262	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1850 and r = \frac{6}{5}$ .	1
11263	Find $a_{8}$ of a geometric progression if $a_{1} = 12 and r = - \frac{1}{3}$ .	1
11264	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = 7 and r = 5$ .	1
11265	Find $a_{1} 0$ of a geometric progression if $a_{1} = 36 and r = \frac{3}{4}$ .	1
11266	Find $a_{1} 2$ of a geometric progression if $a_{1} = 1 and r = \frac{1}{2}$ .	1
11267	Find $a_{1} 2$ of a geometric progression if $a_{1} = 450 and r = \frac{1}{2}$ .	1
11268	Find $a_{5}$ of a geometric progression if $a_{1} = - 17 and r = 5$ .	1
11269	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{1} = 640 and a_{4} = 1080$ .	1
11270	Find $a_{2} 0$ of a geometric progression if $a_{1} = 640 and r = 1.191$ .	1
11271	Find $a_{1} 0$ of a geometric progression if $a_{1} = 5 and r = \frac{5}{2}$ .	1
11272	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = 3 and r = 3$ .	1
11273	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = 3 and r = 3$ .	1
11274	Find the sum of the first $13$ terms of a geometric sequence if $a_{1} = 3 and r = 3$ .	1
11275	Find the sum of the first $13$ terms of a geometric sequence if $a_{1} = 5 and r = 3$ .	1
11276	Find the sum of the first $1$ terms of a geometric sequence if $a_{1} = 6 and r = 3$ .	1
11277	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 0 and r = 2$ .	1
11278	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 4 and r = - 5$ .	1
11279	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 300 and a_{4} = \frac{3}{10}$ .	1
11280	Find $a_{1} 2$ of a geometric progression if $a_{1} = - 9 and r = - 5$ .	1
11281	Find $a_{3}$ of a geometric progression if $a_{1} = 729 and r = \frac{1}{3}$ .	1
11282	Find $a_{5}$ of a geometric progression if $a_{1} = 729 and r = \frac{2}{3}$ .	1
11283	Find $a_{6}$ of a geometric progression if $a_{1} = 729 and r = \frac{1}{4}$ .	1
11284	Find $a_{6}$ of a geometric progression if $a_{1} = 729 and r = \frac{1}{5}$ .	1
11285	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = - 405 and r = \frac{1}{3}$ .	1
11286	Find $a_{7}$ of a geometric progression if $a_{1} = 7 and r = \frac{3}{2}$ .	1
11287	Find $a_{5} 0$ of a geometric progression if $a_{1} = 200 and r = 1.06$ .	1
11288	Find $a_{6} 9$ of a geometric progression if $a_{1} = 200 and r = 1.06$ .	1
11289	Find $a_{2} 0$ of a geometric progression if $a_{1} = 1 and r = \frac{2}{3}$ .	1
11290	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 4 and r = 0.5$ .	1
11291	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 5 and r = - 4$ .	1
11292	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 700 and r = 0.04$ .	1
11293	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 700 and r = \frac{1}{25}$ .	1
11294	Find $a_{7}$ of a geometric progression if $a_{1} = 8 and r = \frac{2}{3}$ .	1
11295	Find $a_{9}$ of a geometric progression if $a_{1} = 3 and r = \frac{3}{2}$ .	1
11296	Find $a_{1} 3$ of a geometric progression if $a_{1} = 10000 and r = 2$ .	1
11297	$a_{1} = 896, r = - 2, a_{1} = ?, r = ?$	1
11298	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = 1 and r = - 1$ .	1
11299	$a_{1} = - 1, r = - 5, a_{1} = ?, r = ?$	1
11300	Find $a_{3}$ of a geometric progression if $a_{1} = 10 and r = \frac{1}{2}$ .	1