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
9251	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 0 and r = \frac{53}{50}$ .	1
9252	Find the sum of the first $16384$ terms of a geometric sequence if $a_{1} = - 16 and r = - 4$ .	1
9253	$a_{1} = 4.1, r = 2, a_{n} = 61.5, n = ?$	1
9254	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = 41000000000 and r = 1.03$ .	1
9255	Find $a_{9} 223372036854775807$ of a geometric progression if $a_{1} = \frac{1}{3} and r = \frac{2}{3}$ .	1
9256	Find $a_{1} 8$ of a geometric progression if $a_{1} = 3 and r = 0.5774$ .	1
9257	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = - 4 and r = - \frac{4}{5}$ .	1
9258	Find first element ( $a_{1}$ ) of a geometic progression if $r = 5 and a_{4} = 500$ .	1
9259	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{4} = 500 and a_{7} = 62500$ .	1
9260	Find $a_{3}$ of a geometric progression if $a_{1} = - 8 and r = - 1$ .	1
9261	Find $a_{3}$ of a geometric progression if $a_{1} = 16 and r = \frac{3}{2}$ .	1
9262	Find $a_{1} 2$ of a geometric progression if $a_{1} = 12 and r = - 5$ .	1
9263	Find $a_{1} 0$ of a geometric progression if $a_{1} = 0.375 and r = 8$ .	1
9264	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1000 and r = \frac{1}{2}$ .	1
9265	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{4}{9} and r = - 3$ .	1
9266	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 270 and r = \frac{1}{3}$ .	1
9267	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 3 and r = \frac{1}{5}$ .	1
9268	Find first element ( $a_{1}$ ) of a geometic progression if $r = \frac{2}{3} and a_{5} = 32$ .	1
9269	Find $a_{2}$ of a geometric progression if $a_{1} = 75000 and r = \frac{1}{2}$ .	1
9270	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = 75000 and r = \frac{1}{2}$ .	1
9271	Find the sum of the first $40$ terms of a geometric sequence if $a_{1} = 75000 and r = \frac{1}{2}$ .	1
9272	Find the sum of the first $40$ terms of a geometric sequence if $a_{1} = 75000 and r = \frac{2}{3}$ .	1
9273	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 256 and r = - \frac{1}{4}$ .	1
9274	Find $a_{1} 6$ of a geometric progression if $a_{1} = 10 and r = 9$ .	1
9275	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{9}{10}$ .	1
9276	Find $a_{4}$ of a geometric progression if $a_{1} = 9 and r = - \frac{1}{3}$ .	1
9277	Find $a_{9} 9999999$ of a geometric progression if $a_{1} = 1 and r = \frac{4}{3}$ .	1
9278	Find $a_{1}$ of a geometric progression if $a_{1} = 1 and r = \frac{2}{3}$ .	1
9279	$a_{1} = 1, r = 2, a_{n} = 2, n = ?$	1
9280	$a_{1} = 1, r = 2, S_{n} = 16, n = ?$	1
9281	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 48 and r = \frac{5}{4}$ .	1
9282	Find $a_{1} 0$ of a geometric progression if $a_{1} = 48000 and r = 1.05$ .	1
9283	Find $a_{2}$ of a geometric progression if $a_{1} = 9 and r = - \frac{1}{2}$ .	1
9284	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{8} = 512 and a_{3} = 16$ .	1
9285	$a_{1} = \frac{8}{3}, r = \frac{3}{2}, S_{n} = 2500, n = ?$	1
9286	Find $a_{9}$ of a geometric progression if $a_{1} = 1024 and r = \frac{1}{2}$ .	1
9287	Find $a_{6}$ of a geometric progression if $a_{1} = 32 and r = \frac{3}{2}$ .	1
9288	Find $a_{3}$ of a geometric progression if $a_{1} = - 1 and r = \frac{1}{2}$ .	1
9289	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 12 and r = 2$ .	1
9290	Find $a_{9}$ of a geometric progression if $a_{1} = 7300000000 and r = 1.012$ .	1
9291	Find $a_{6}$ of a geometric progression if $a_{1} = - 4 and r = 4$ .	1
9292	Find $a_{6}$ of a geometric progression if $a_{1} = - 4 and r = 3$ .	1
9293	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 18 and r = - \frac{1}{2}$ .	1
9294	Find $a_{6}$ of a geometric progression if $a_{1} = 2 and r = 3$ .	1
9295	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 384 and r = \frac{5}{4}$ .	1
9296	Find $a_{2} 4$ of a geometric progression if $a_{1} = 96 and r = 48$ .	1
9297	Find $a_{7}$ of a geometric progression if $a_{1} = 7 and r = 4$ .	1
9298	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 2 and a_{5} = \frac{1}{4}$ .	1
9299	Find $a_{6}$ of a geometric progression if $a_{1} = 40 and r = \frac{1}{10}$ .	1
9300	Find first element ( $a_{1}$ ) of a geometic progression if $r = - \frac{1}{2} and a_{3} = 8$ .	1