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
10751	Find $a_{1} 0$ of a geometric progression if $a_{1} = 10000 and r = \frac{11}{10}$ .	1
10752	Find $a_{5}$ of a geometric progression if $a_{1} = 10000 and r = \frac{3}{2}$ .	1
10753	Find $a_{8}$ of a geometric progression if $a_{1} = 15 and r = 5$ .	1
10754	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = - 5 and r = \frac{1}{2}$ .	1
10755	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = - 4 and r = - 5$ .	1
10756	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1875 and r = \frac{2}{5}$ .	1
10757	Find $a_{3}$ of a geometric progression if $a_{1} = 3200 and r = \frac{1}{4}$ .	1
10758	Find $a_{8}$ of a geometric progression if $a_{1} = 3200 and r = \frac{1}{4}$ .	1
10759	Find $a_{1} 3$ of a geometric progression if $a_{1} = 6 and r = - 6$ .	1
10760	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 64 and r = \frac{3}{4}$ .	1
10761	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 30 and r = \frac{1}{2}$ .	1
10762	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{4} = 512 and a_{7} = 32768$ .	1
10763	Find $a_{1}$ of a geometric progression if $a_{1} = 80 and r = 20$ .	1
10764	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 1 and a_{5} = 64$ .	1
10765	Find $a_{6}$ of a geometric progression if $a_{1} = 120 and r = 25.2$ .	1
10766	Find $a_{1} 4$ of a geometric progression if $a_{1} = 3 and r = - 3$ .	1
10767	Find $a_{1} 4$ of a geometric progression if $a_{1} = 4 and r = - 3$ .	1
10768	Find $a_{1} 00000$ of a geometric progression if $a_{1} = 4 and r = \frac{3}{2}$ .	1
10769	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 467426 and r = 0.83$ .	1
10770	Find the sum of the first $99$ terms of a geometric sequence if $a_{1} = 1 and r = - 1$ .	1
10771	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = - 12 and r = - \frac{1}{2}$ .	1
10772	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{2}$ .	1
10773	Find the sum of the first $66$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{2}$ .	1
10774	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{2}$ .	1
10775	Find the sum of the first $9223372036854775807$ terms of a geometric sequence if $a_{1} = 150 and r = - 0.4$ .	1
10776	Find $a_{5}$ of a geometric progression if $a_{1} = 2 and r = - \frac{1}{3}$ .	1
10777	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = \frac{5}{2} and r = 2$ .	1
10778	Find $a_{4}$ of a geometric progression if $a_{1} = - \frac{8}{3} and r = - \frac{1}{2}$ .	1
10779	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{1}{5} and r = \frac{1}{10}$ .	1
10780	Find $a_{5}$ of a geometric progression if $a_{1} = 7 and r = \frac{3}{2}$ .	1
10781	Find $a_{7}$ of a geometric progression if $a_{1} = 5 and r = \frac{3}{2}$ .	1
10782	Find $a_{5}$ of a geometric progression if $a_{1} = 7 and r = \frac{1}{3}$ .	1
10783	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 3 and r = 0.95$ .	1
10784	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{3}{5} and r = - 3$ .	1
10785	Find $a_{7}$ of a geometric progression if $a_{1} = - 1 and r = 1$ .	1
10786	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{3}{4}$ .	1
10787	Find $a_{1} 4$ of a geometric progression if $a_{1} = 1 and r = - \frac{1}{2}$ .	1
10788	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 6500 and r = \frac{107}{100}$ .	1
10789	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 6955 and r = 1.07$ .	1
10790	Find $a_{1} 00$ of a geometric progression if $a_{1} = 1 and r = 0.367$ .	1
10791	Find $a_{1} 00$ of a geometric progression if $a_{1} = 100 and r = 0.367$ .	1
10792	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 0 and r = 12$ .	1
10793	Find $a_{4}$ of a geometric progression if $a_{1} = 50 and r = \frac{1}{2}$ .	1
10794	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 50 and r = \frac{1}{2}$ .	1
10795	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 3 and a_{4} = 125$ .	1
10796	Find $a_{9} 999$ of a geometric progression if $a_{1} = 500000 and r = 0.99$ .	1
10797	Find $a_{9} 99$ of a geometric progression if $a_{1} = 500000 and r = 0.99$ .	1
10798	Find $a_{6}$ of a geometric progression if $a_{1} = 2000 and r = \frac{1}{2}$ .	1
10799	Find $a_{6}$ of a geometric progression if $a_{1} = 2000 and r = \frac{1}{10}$ .	1
10800	Find $a_{6}$ of a geometric progression if $a_{1} = \frac{3}{2} and r = \frac{1}{2}$ .	1