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
10101	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 270 and r = \frac{1}{3}$ .	1
10102	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 3 and r = \frac{1}{5}$ .	1
10103	Find first element ( $a_{1}$ ) of a geometic progression if $r = \frac{2}{3} and a_{5} = 32$ .	1
10104	Find $a_{2}$ of a geometric progression if $a_{1} = 75000 and r = \frac{1}{2}$ .	1
10105	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = 75000 and r = \frac{1}{2}$ .	1
10106	Find the sum of the first $40$ terms of a geometric sequence if $a_{1} = 75000 and r = \frac{1}{2}$ .	1
10107	Find the sum of the first $40$ terms of a geometric sequence if $a_{1} = 75000 and r = \frac{2}{3}$ .	1
10108	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 3 and r = - 2$ .	1
10109	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 256 and r = - \frac{1}{4}$ .	1
10110	Find $a_{1} 6$ of a geometric progression if $a_{1} = 10 and r = 9$ .	1
10111	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{9}{10}$ .	1
10112	Find $a_{4}$ of a geometric progression if $a_{1} = 9 and r = - \frac{1}{3}$ .	1
10113	Find $a_{9} 9999999$ of a geometric progression if $a_{1} = 1 and r = \frac{4}{3}$ .	1
10114	Find $a_{1}$ of a geometric progression if $a_{1} = 1 and r = \frac{2}{3}$ .	1
10115	$a_{1} = 1, r = 2, a_{n} = 2, n = ?$	1
10116	$a_{1} = 1, r = 2, S_{n} = 16, n = ?$	1
10117	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 48 and r = \frac{5}{4}$ .	1
10118	Find $a_{1} 0$ of a geometric progression if $a_{1} = 48000 and r = 1.05$ .	1
10119	Find $a_{2}$ of a geometric progression if $a_{1} = 9 and r = - \frac{1}{2}$ .	1