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
9601	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = 5 and r = 5$ .	1
9602	Find $a_{4}$ of a geometric progression if $a_{1} = 10 and r = \frac{4}{5}$ .	1
9603	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 10 and r = \frac{4}{5}$ .	1
9604	Find the sum of the first $100$ terms of a geometric sequence if $a_{1} = 10 and r = 0.8$ .	1
9605	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 147 and r = 1000$ .	1
9606	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = 147 and r = 1000$ .	1
9607	Find the sum of the first $37$ terms of a geometric sequence if $a_{1} = 1 and r = 0.9801$ .	1
9608	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{100}{81} and r = \frac{10}{9}$ .	1
9609	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{100}{81} and r = \frac{9}{10}$ .	1
9610	Find $a_{7}$ of a geometric progression if $a_{1} = 50 and r = \frac{1}{2}$ .	1
9611	Find $a_{7}$ of a geometric progression if $a_{1} = 50 and r = \frac{3}{2}$ .	1
9612	Find $a_{9}$ of a geometric progression if $a_{1} = 8 and r = - \frac{1}{10}$ .	1
9613	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 8 and r = - \frac{1}{10}$ .	1
9614	Find $a_{1} 0$ of a geometric progression if $a_{1} = 10 and r = 5$ .	1
9615	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 10 and r = 5$ .	1
9616	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = \frac{2}{5} and r = 0.7753$ .	1
9617	Find $a_{1} 7$ of a geometric progression if $a_{1} = \frac{2}{5} and r = 1.189$ .	1
9618	Find $a_{5}$ of a geometric progression if $a_{1} = 16807 and r = - 7$ .	1
9619	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 16807 and r = - 7$ .	1
9620	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 16807 and r = - 7$ .	1
9621	Find $a_{1} 4$ of a geometric progression if $a_{1} = 6144 and r = \frac{1}{2}$ .	1
9622	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = 1 and r = 1.333$ .	1
9623	Find $a_{5}$ of a geometric progression if $a_{1} = 483 and r = 17$ .	1
9624	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 1 and a_{4} = 16$ .	1
9625	Find $a_{1} 30$ of a geometric progression if $a_{1} = 1 and r = 0.02$ .	1
9626	Find $a_{1} 30$ of a geometric progression if $a_{1} = 1 and r = 1.02$ .	1
9627	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{1} = 15 and a_{100} = 307$ .	1
9628	Find the sum of the first $25$ terms of a geometric sequence if $a_{1} = 100 and r = 1.033$ .	1
9629	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = 360000 and r = 1.2$ .	1
9630	Find $a_{5}$ of a geometric progression if $a_{1} = 60000 and r = 1.035$ .	1
9631	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{12} = 48 and a_{19} = \frac{3}{4}$ .	1
9632	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{1}{8} and r = 4$ .	1
9633	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 10000 and r = \frac{11}{10}$ .	1
9634	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = \frac{2}{3} and r = \frac{2}{3}$ .	1
9635	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 20000 and r = \frac{11}{10}$ .	1
9636	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 24000 and r = \frac{11}{10}$ .	1
9637	Find $a_{6} 0$ of a geometric progression if $a_{1} = 1 and r = 1.011$ .	1
9638	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 16 and r = \frac{5}{2}$ .	1
9639	Find $a_{5}$ of a geometric progression if $a_{1} = 608 and r = \frac{1}{2}$ .	1
9640	Find $a_{4}$ of a geometric progression if $a_{1} = 2 and r = - 11$ .	1
9641	Find $a_{6}$ of a geometric progression if $a_{1} = 495000 and r = \frac{1}{10}$ .	1
9642	$a_{1} = 256, r = \frac{3}{4}, S_{n} = 13, n = ?$	1
9643	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 120 and r = \frac{1}{4}$ .	1
9644	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 14 and r = \frac{11}{50}$ .	1
9645	Find $a_{1} 0$ of a geometric progression if $a_{1} = 16 and r = - 6$ .	1
9646	Find $a_{2}$ of a geometric progression if $a_{1} = 16 and r = - 6$ .	1
9647	Find $a_{2}$ of a geometric progression if $a_{1} = 16 and r = - \frac{3}{2}$ .	1
9648	Find $a_{3}$ of a geometric progression if $a_{1} = 16 and r = - \frac{3}{2}$ .	1
9649	Find first element ( $a_{1}$ ) of a geometic progression if $r = 4 and a_{5} = 1792$ .	1
9650	Find $a_{2} 5$ of a geometric progression if $a_{1} = 5 and r = 2$ .	1