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
11051	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 2500 and r = \frac{6}{5}$ .	1
11052	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 30000 and r = \frac{6}{5}$ .	1
11053	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1 and r = 1$ .	1
11054	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 1 and r = - 0.3854$ .	1
11055	Find $a_{3} 0$ of a geometric progression if $a_{1} = 100 and r = 0.9117$ .	1
11056	Find $a_{2}$ of a geometric progression if $a_{1} = 5 and r = \frac{1}{4}$ .	1
11057	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 125 and a_{4} = 27$ .	1
11058	$a_{1} = 125, r = \frac{3}{5}, a_{1} = ?, r = ?$	1
11059	Find $a_{9}$ of a geometric progression if $a_{1} = \frac{1}{4} and r = 2$ .	1
11060	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = \frac{1}{4} and r = 2$ .	1
11061	Find $a_{3} 0$ of a geometric progression if $a_{1} = 100000 and r = 1.05$ .	1
11062	Find $a_{3} 1$ of a geometric progression if $a_{1} = 0.01 and r = 3$ .	1
11063	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 0.01 and r = 3$ .	1
11064	Find $a_{5}$ of a geometric progression if $a_{1} = 0.01 and r = 3$ .	1
11065	Find $a_{5}$ of a geometric progression if $a_{1} = 8000 and r = 0.25$ .	1
11066	Find $a_{9}$ of a geometric progression if $a_{1} = 3 and r = \frac{8}{3}$ .	1
11067	Find $a_{1} 4$ of a geometric progression if $a_{1} = 3132676 and r = 1.007$ .	1
11068	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 10000 and r = 1.07$ .	1
11069	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 10000 and r = 0.07$ .	1
11070	Find $a_{6}$ of a geometric progression if $a_{1} = 10000 and r = 0.07$ .	1
11071	Find $a_{6}$ of a geometric progression if $a_{1} = 10000 and r = 1.07$ .	1
11072	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 10000 and r = 1.07$ .	1
11073	Find $a_{1} 8$ of a geometric progression if $a_{1} = \frac{1}{2048} and r = 2$ .	1
11074	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 100000 and r = 0.06$ .	1
11075	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1 and r = - 5$ .	1
11076	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 18 and r = \frac{1}{9}$ .	1
11077	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = \frac{2}{9} and r = \frac{3}{2}$ .	1
11078	Find the sum of the first $1000$ terms of a geometric sequence if $a_{1} = \frac{1}{100} and r = \frac{1}{100}$ .	1
11079	$a_{1} = 1, r = 2, a_{n} = 10, n = ?$	1
11080	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 6 and r = \frac{5}{7}$ .	1
11081	Find $a_{6}$ of a geometric progression if $a_{1} = \frac{1}{121} and r = \frac{1}{4}$ .	1
11082	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = 4 and r = 2$ .	1
11083	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{3}{2}$ .	1
11084	Find $a_{2} 0$ of a geometric progression if $a_{1} = - 7 and r = - 3$ .	1
11085	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{7} = 100 and a_{5} = 25$ .	1
11086	Find $a_{1} 4$ of a geometric progression if $a_{1} = 7 and r = \frac{3}{2}$ .	1
11087	$a_{1} = 3, r = 3, a_{n} = 59049, n = ?$	1
11088	Find the sum of the first $10000$ terms of a geometric sequence if $a_{1} = 1 and r = 1.1$ .	1
11089	Find the sum of the first $10000$ terms of a geometric sequence if $a_{1} = 1 and r = 0.9$ .	1
11090	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 18 and r = - \frac{1}{2}$ .	1
11091	Find the sum of the first $25$ terms of a geometric sequence if $a_{1} = \frac{1}{4} and r = \frac{1}{2}$ .	1
11092	Find $a_{2} 3$ of a geometric progression if $a_{1} = - 2 and r = - 2$ .	1
11093	Find $a_{2} 0$ of a geometric progression if $a_{1} = 1 and r = \frac{100}{103}$ .	1
11094	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = 9 and r = 3$ .	1
11095	Find $a_{4}$ of a geometric progression if $a_{1} = 24 and r = \frac{1}{3}$ .	1
11096	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{21}{20}$ .	1
11097	Find $a_{5}$ of a geometric progression if $a_{1} = 20 and r = 1.5$ .	1
11098	Find $a_{5}$ of a geometric progression if $a_{1} = 25 and r = 1.5$ .	1
11099	Find $a_{5}$ of a geometric progression if $a_{1} = 30 and r = 1.5$ .	1
11100	Find $a_{7}$ of a geometric progression if $a_{1} = 30 and r = 1.5$ .	1