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
10301	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 467426 and r = 0.83$ .	1
10302	Find the sum of the first $99$ terms of a geometric sequence if $a_{1} = 1 and r = - 1$ .	1
10303	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = - 12 and r = - \frac{1}{2}$ .	1
10304	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{2}$ .	1
10305	Find the sum of the first $66$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{2}$ .	1
10306	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{2}$ .	1
10307	Find the sum of the first $9223372036854775807$ terms of a geometric sequence if $a_{1} = 150 and r = - 0.4$ .	1
10308	Find $a_{5}$ of a geometric progression if $a_{1} = 2 and r = - \frac{1}{3}$ .	1
10309	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = \frac{5}{2} and r = 2$ .	1
10310	Find $a_{4}$ of a geometric progression if $a_{1} = - \frac{8}{3} and r = - \frac{1}{2}$ .	1
10311	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{1}{5} and r = \frac{1}{10}$ .	1
10312	Find $a_{5}$ of a geometric progression if $a_{1} = 7 and r = \frac{3}{2}$ .	1
10313	Find $a_{7}$ of a geometric progression if $a_{1} = 5 and r = \frac{3}{2}$ .	1
10314	Find $a_{5}$ of a geometric progression if $a_{1} = 7 and r = \frac{1}{3}$ .	1
10315	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 3 and r = 0.95$ .	1
10316	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{3}{5} and r = - 3$ .	1
10317	Find $a_{7}$ of a geometric progression if $a_{1} = - 1 and r = 1$ .	1
10318	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{3}{4}$ .	1
10319	Find $a_{1} 4$ of a geometric progression if $a_{1} = 1 and r = - \frac{1}{2}$ .	1
10320	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 6500 and r = \frac{107}{100}$ .	1
10321	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 6955 and r = 1.07$ .	1
10322	Find $a_{1} 00$ of a geometric progression if $a_{1} = 1 and r = 0.367$ .	1
10323	Find $a_{1} 00$ of a geometric progression if $a_{1} = 100 and r = 0.367$ .	1
10324	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 0 and r = 12$ .	1
10325	Find $a_{4}$ of a geometric progression if $a_{1} = 50 and r = \frac{1}{2}$ .	1
10326	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 50 and r = \frac{1}{2}$ .	1
10327	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 3 and a_{4} = 125$ .	1
10328	Find $a_{9} 999$ of a geometric progression if $a_{1} = 500000 and r = 0.99$ .	1
10329	Find $a_{9} 99$ of a geometric progression if $a_{1} = 500000 and r = 0.99$ .	1
10330	Find $a_{6}$ of a geometric progression if $a_{1} = 2000 and r = \frac{1}{2}$ .	1
10331	Find $a_{6}$ of a geometric progression if $a_{1} = 2000 and r = \frac{1}{10}$ .	1
10332	Find $a_{6}$ of a geometric progression if $a_{1} = \frac{3}{2} and r = \frac{1}{2}$ .	1
10333	Find $a_{8}$ of a geometric progression if $a_{1} = 3 and r = 9$ .	1
10334	Find $a_{4}$ of a geometric progression if $a_{1} = 222 and r = \frac{11}{10}$ .	1
10335	$a_{1} = 1, r = 3, S_{n} = 22, n = ?$	1
10336	$a_{1} = 12000, r = \frac{11}{10}, a_{n} = 100, n = ?$	1
10337	Find the sum of the first $13$ terms of a geometric sequence if $a_{1} = - 7 and r = 4$ .	1
10338	Find $a_{3}$ of a geometric progression if $a_{1} = 10 and r = \frac{1}{10}$ .	1
10339	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 10 and r = \frac{1}{10}$ .	1
10340	Find $a_{9}$ of a geometric progression if $a_{1} = - 8 and r = - 4$ .	1
10341	Find $a_{1} 0$ of a geometric progression if $a_{1} = \frac{1}{243} and r = \frac{1}{3}$ .	1
10342	Find $a_{9}$ of a geometric progression if $a_{1} = 27 and r = \frac{1}{3}$ .	1
10343	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = - 8 and r = - 4$ .	1
10344	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 81 and r = - \frac{1}{3}$ .	1
10345	Find $a_{1} 7$ of a geometric progression if $a_{1} = 1 and r = 9$ .	1
10346	Find $a_{1} 7$ of a geometric progression if $a_{1} = 6 and r = - 3$ .	1
10347	Find $a_{6}$ of a geometric progression if $a_{1} = 15 and r = \frac{2}{3}$ .	1
10348	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{49}{8} and r = \frac{7}{8}$ .	1
10349	Find $a_{1} 9$ of a geometric progression if $a_{1} = - 3 and r = - 2$ .	1
10350	Find $a_{1} 3$ of a geometric progression if $a_{1} = - 3 and r = - 2$ .	1