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
9651	Find $a_{9}$ of a geometric progression if $a_{1} = 1200 and r = 0.003$ .	1
9652	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 1200 and r = 1.003$ .	1
9653	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 1200 and r = \frac{1003}{1000}$ .	1
9654	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 2 and r = 6$ .	1
9655	Find $a_{1} 4$ of a geometric progression if $a_{1} = 1 and r = - 2$ .	1
9656	Find $a_{1} 4$ of a geometric progression if $a_{1} = 5 and r = - 2$ .	1
9657	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = - 6 and r = - 0.5$ .	1
9658	Find $a_{5}$ of a geometric progression if $a_{1} = 2000 and r = \frac{1}{5}$ .	1
9659	Find $a_{5}$ of a geometric progression if $a_{1} = 40000 and r = \frac{26}{25}$ .	1
9660	$a_{1} = - \frac{1}{2}, r = - 2, a_{1} = ?, r = ?$	1
9661	Find $a_{5}$ of a geometric progression if $a_{1} = 256 and r = \frac{1}{2}$ .	1
9662	Find $a_{1} 3$ of a geometric progression if $a_{1} = 7 and r = \frac{1}{7}$ .	1
9663	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 5 and r = - \frac{1}{5}$ .	1
9664	Find $a_{7}$ of a geometric progression if $a_{1} = 6 and r = \frac{1}{2}$ .	1
9665	Find $a_{8}$ of a geometric progression if $a_{1} = 648 and r = \frac{1}{3}$ .	1
9666	Find $a_{2} 5$ of a geometric progression if $a_{1} = 1 and r = \frac{1}{2}$ .	1
9667	Find the sum of the first $25$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{2}$ .	1
9668	Find $a_{4}$ of a geometric progression if $a_{1} = 1 and r = - 1$ .	1
9669	Find $a_{3} 0$ of a geometric progression if $a_{1} = 100 and r = \frac{4}{5}$ .	1
9670	Find $a_{1} 4$ of a geometric progression if $a_{1} = 7 and r = 3$ .	1
9671	Find $a_{1} 2$ of a geometric progression if $a_{1} = 3 and r = 2$ .	1
9672	Find $a_{1} 1$ of a geometric progression if $a_{1} = 6 and r = 3$ .	1
9673	Find $a_{3}$ of a geometric progression if $a_{1} = 3 and r = \frac{3}{2}$ .	1
9674	Find $a_{9}$ of a geometric progression if $a_{1} = 6 and r = \frac{2}{3}$ .	1
9675	Find $a_{5}$ of a geometric progression if $a_{1} = - 5 and r = 5$ .	1
9676	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 0.403 and r = \frac{1}{2}$ .	1
9677	Find $a_{3} 65$ of a geometric progression if $a_{1} = 100 and r = 1.01$ .	1
9678	Find $a_{3} 65$ of a geometric progression if $a_{1} = 100 and r = 1.02$ .	1
9679	Find $a_{1} 00$ of a geometric progression if $a_{1} = 20 and r = 1.02$ .	1
9680	Find $a_{2} 0$ of a geometric progression if $a_{1} = 100 and r = 1.02$ .	1
9681	Find $a_{3} 0$ of a geometric progression if $a_{1} = 100 and r = 1.02$ .	1
9682	Find $a_{3} 0$ of a geometric progression if $a_{1} = 50 and r = 1.02$ .	1
9683	Find $a_{1} 5$ of a geometric progression if $a_{1} = 135 and r = \frac{1}{3}$ .	1
9684	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 20 and a_{5} = 2500$ .	1
9685	Find common ratio ( $r$ ) in geometic progression if $a_{1} = \frac{1}{3} and a_{2} = \frac{1}{5}$ .	1
9686	Find $a_{1}$ of a geometric progression if $a_{1} = - 4 and r = 6$ .	1
9687	Find $a_{1} 2$ of a geometric progression if $a_{1} = 100 and r = 1.135$ .	1
9688	Find $a_{6}$ of a geometric progression if $a_{1} = \frac{1}{3} and r = \frac{1}{3}$ .	1
9689	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{1}{3} and r = \frac{1}{3}$ .	1
9690	Find $a_{4}$ of a geometric progression if $a_{1} = 128 and r = \frac{1}{2}$ .	1
9691	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{2}{3} and r = - \frac{1}{3}$ .	1
9692	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 64 and r = - 0.75$ .	1
9693	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 0 and r = 2$ .	1
9694	Find $a_{5}$ of a geometric progression if $a_{1} = 10000 and r = \frac{4}{5}$ .	1
9695	Find first element ( $a_{1}$ ) of a geometic progression if $r = 5 and a_{6} = 15$ .	1
9696	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 100 and r = \frac{1}{10}$ .	1
9697	Find $a_{8}$ of a geometric progression if $a_{1} = 1000 and r = 2$ .	1
9698	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{3}{5} and r = \frac{1}{3}$ .	1
9699	Find $a_{1} 1$ of a geometric progression if $a_{1} = - 1 and r = - 7$ .	1
9700	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 60000 and r = \frac{23}{20}$ .	1