Geometric sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Geometric sequences.

Select category

ID	Problem	Count
9701	Find the sum of the first $480$ terms of a geometric sequence if $a_{1} = 500 and r = 1.006$ .	1
9702	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{5}{343} and r = 7$ .	1
9703	Find $a_{2}$ of a geometric progression if $a_{1} = 3 and r = - 2$ .	1
9704	Find $a_{1} 0$ of a geometric progression if $a_{1} = 64 and r = - \frac{1}{4}$ .	1
9705	$a_{1} = 6, r = 2, a_{n} = 8, n = ?$	1
9706	Find $a_{6} 0$ of a geometric progression if $a_{1} = 100 and r = 1.005$ .	1
9707	Find $a_{2}$ of a geometric progression if $a_{1} = 50 and r = 25$ .	1
9708	Find the sum of the first $360$ terms of a geometric sequence if $a_{1} = 51 and r = 1.02$ .	1
9709	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 7 and r = 1$ .	1
9710	$a_{1} = 1133, r = 0.00967, S_{n} = 37890, n = ?$	1
9711	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 1500 and r = 2$ .	1
9712	Find $a_{2}$ of a geometric progression if $a_{1} = 1000 and r = 2$ .	1
9713	Find $a_{2} 0$ of a geometric progression if $a_{1} = 1000 and r = 2$ .	1
9714	Find $a_{1} 6$ of a geometric progression if $a_{1} = 1000 and r = 2$ .	1
9715	Find $a_{4}$ of a geometric progression if $a_{1} = - 3 and r = - 3$ .	1
9716	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{9}{5}$ .	1
9717	Find $a_{8}$ of a geometric progression if $a_{1} = 4 and r = 3$ .	1
9718	Find $a_{7}$ of a geometric progression if $a_{1} = 3 and r = 3$ .	1
9719	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 3 and r = 3$ .	1
9720	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 4 and r = 3$ .	1
9721	Find $a_{8}$ of a geometric progression if $a_{1} = 18 and r = 1.66$ .	1
9722	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{3}{16} and r = \frac{27}{64}$ .	1
9723	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = - 2 and r = - 4$ .	1
9724	Find $a_{1} 4$ of a geometric progression if $a_{1} = 6 and r = - 3$ .	1
9725	Find $a_{7}$ of a geometric progression if $a_{1} = 18 and r = - 3$ .	1
9726	Find $a_{6}$ of a geometric progression if $a_{1} = 400 and r = \frac{1}{5}$ .	1
9727	Find the sum of the first $36$ terms of a geometric sequence if $a_{1} = 1 and r = 1.005$ .	1
9728	Find the sum of the first $36$ terms of a geometric sequence if $a_{1} = 36 and r = 1.005$ .	1
9729	Find $a_{5}$ of a geometric progression if $a_{1} = 0 and r = - 4$ .	1
9730	Find $a_{2}$ of a geometric progression if $a_{1} = - \frac{1}{100} and r = - 10$ .	1
9731	Find $a_{7}$ of a geometric progression if $a_{1} = 625 and r = \frac{1}{5}$ .	1
9732	Find first element ( $a_{1}$ ) of a geometic progression if $r = - 2 and a_{8} = 124$ .	1
9733	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{7}{4} and r = \frac{7}{4}$ .	1
9734	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 0 and r = - \frac{1}{3}$ .	1
9735	Find the sum of the first $100$ terms of a geometric sequence if $a_{1} = 1 and r = - \frac{1}{3}$ .	1
9736	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 40000 and r = \frac{21}{20}$ .	1
9737	Find $a_{1} 0$ of a geometric progression if $a_{1} = 2 and r = 10$ .	1
9738	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = - \frac{1}{3} and r = - \frac{1}{3}$ .	1
9739	Find $a_{7}$ of a geometric progression if $a_{1} = 1 and r = 2$ .	1
9740	Find $a_{1} 4$ of a geometric progression if $a_{1} = 1 and r = - \frac{1}{5}$ .	1
9741	Find $a_{1} 3$ of a geometric progression if $a_{1} = 1 and r = \frac{1}{2}$ .	1
9742	Find $a_{1} 2$ of a geometric progression if $a_{1} = 5 and r = - \frac{1}{5}$ .	1
9743	Find $a_{1} 5$ of a geometric progression if $a_{1} = 1000 and r = \frac{3}{2}$ .	1
9744	Find $a_{2} 1$ of a geometric progression if $a_{1} = 1000 and r = 1.5$ .	1
9745	Find $a_{2} 5$ of a geometric progression if $a_{1} = 1000 and r = 1.5$ .	1
9746	Find $a_{2} 3$ of a geometric progression if $a_{1} = 1000 and r = 1.5$ .	1
9747	Find $a_{1} 44$ of a geometric progression if $a_{1} = 1000 and r = 1.5$ .	1
9748	Find $a_{1} 00$ of a geometric progression if $a_{1} = 1000 and r = 1.5$ .	1
9749	Find $a_{6}$ of a geometric progression if $a_{1} = 5 and r = 5$ .	1
9750	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{17}{250} and r = \frac{17}{25}$ .	1