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
10951	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 2 and a_{5} = \frac{13}{8}$ .	1
10952	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = \frac{1}{5} and r = \frac{1}{2}$ .	1
10953	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 2500 and r = \frac{6}{5}$ .	1
10954	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 30000 and r = \frac{6}{5}$ .	1
10955	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1 and r = 1$ .	1
10956	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 1 and r = - 0.3854$ .	1
10957	Find $a_{3} 0$ of a geometric progression if $a_{1} = 100 and r = 0.9117$ .	1
10958	Find $a_{2}$ of a geometric progression if $a_{1} = 5 and r = \frac{1}{4}$ .	1
10959	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 125 and a_{4} = 27$ .	1
10960	$a_{1} = 125, r = \frac{3}{5}, a_{1} = ?, r = ?$	1
10961	Find $a_{9}$ of a geometric progression if $a_{1} = \frac{1}{4} and r = 2$ .	1
10962	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = \frac{1}{4} and r = 2$ .	1
10963	Find $a_{3} 0$ of a geometric progression if $a_{1} = 100000 and r = 1.05$ .	1
10964	Find $a_{3} 1$ of a geometric progression if $a_{1} = 0.01 and r = 3$ .	1
10965	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 0.01 and r = 3$ .	1
10966	Find $a_{5}$ of a geometric progression if $a_{1} = 0.01 and r = 3$ .	1
10967	Find $a_{5}$ of a geometric progression if $a_{1} = 8000 and r = 0.25$ .	1
10968	Find $a_{9}$ of a geometric progression if $a_{1} = 3 and r = \frac{8}{3}$ .	1
10969	Find $a_{1} 4$ of a geometric progression if $a_{1} = 3132676 and r = 1.007$ .	1
10970	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 10000 and r = 1.07$ .	1
10971	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 10000 and r = 0.07$ .	1
10972	Find $a_{6}$ of a geometric progression if $a_{1} = 10000 and r = 0.07$ .	1
10973	Find $a_{6}$ of a geometric progression if $a_{1} = 10000 and r = 1.07$ .	1
10974	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 10000 and r = 1.07$ .	1
10975	Find $a_{1} 8$ of a geometric progression if $a_{1} = \frac{1}{2048} and r = 2$ .	1
10976	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 100000 and r = 0.06$ .	1
10977	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1 and r = - 5$ .	1
10978	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 18 and r = \frac{1}{9}$ .	1
10979	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = \frac{2}{9} and r = \frac{3}{2}$ .	1
10980	Find the sum of the first $1000$ terms of a geometric sequence if $a_{1} = \frac{1}{100} and r = \frac{1}{100}$ .	1
10981	$a_{1} = 1, r = 2, a_{n} = 10, n = ?$	1
10982	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 6 and r = \frac{5}{7}$ .	1
10983	Find $a_{6}$ of a geometric progression if $a_{1} = \frac{1}{121} and r = \frac{1}{4}$ .	1
10984	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = 4 and r = 2$ .	1
10985	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{3}{2}$ .	1
10986	Find $a_{2} 0$ of a geometric progression if $a_{1} = - 7 and r = - 3$ .	1
10987	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{7} = 100 and a_{5} = 25$ .	1
10988	Find $a_{1} 4$ of a geometric progression if $a_{1} = 7 and r = \frac{3}{2}$ .	1
10989	$a_{1} = 3, r = 3, a_{n} = 59049, n = ?$	1
10990	Find the sum of the first $10000$ terms of a geometric sequence if $a_{1} = 1 and r = 1.1$ .	1
10991	Find the sum of the first $10000$ terms of a geometric sequence if $a_{1} = 1 and r = 0.9$ .	1
10992	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 18 and r = - \frac{1}{2}$ .	1
10993	Find the sum of the first $25$ terms of a geometric sequence if $a_{1} = \frac{1}{4} and r = \frac{1}{2}$ .	1
10994	Find $a_{2} 3$ of a geometric progression if $a_{1} = - 2 and r = - 2$ .	1
10995	Find $a_{2} 0$ of a geometric progression if $a_{1} = 1 and r = \frac{100}{103}$ .	1
10996	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = 9 and r = 3$ .	1
10997	Find $a_{4}$ of a geometric progression if $a_{1} = 24 and r = \frac{1}{3}$ .	1
10998	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{21}{20}$ .	1
10999	Find $a_{5}$ of a geometric progression if $a_{1} = 20 and r = 1.5$ .	1
11000	Find $a_{5}$ of a geometric progression if $a_{1} = 25 and r = 1.5$ .	1