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
10851	Find $a_{1} 0$ of a geometric progression if $a_{1} = 75 and r = 4$ .	1
10852	Find $a_{9}$ of a geometric progression if $a_{1} = 75 and r = 4$ .	1
10853	Find $a_{1} 1$ of a geometric progression if $a_{1} = 20 and r = 3$ .	1
10854	Find $a_{1} 1$ of a geometric progression if $a_{1} = 400 and r = - 4$ .	1
10855	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 7 and r = 6$ .	1
10856	Find $a_{4}$ of a geometric progression if $a_{1} = - 1 and r = 3$ .	1
10857	Find $a_{5}$ of a geometric progression if $a_{1} = 6 and r = 6$ .	1
10858	Find $a_{3}$ of a geometric progression if $a_{1} = 512 and r = - \frac{1}{4}$ .	1
10859	Find $a_{4}$ of a geometric progression if $a_{1} = 512 and r = - \frac{1}{4}$ .	1
10860	Find $a_{5}$ of a geometric progression if $a_{1} = 512 and r = - \frac{1}{4}$ .	1
10861	Find $a_{6}$ of a geometric progression if $a_{1} = 512 and r = - \frac{1}{4}$ .	1
10862	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{6} = 750 and a_{10} = 3200$ .	1
10863	$a_{1} = 324, r = 3, a_{1} = ?, r = ?$	1
10864	Find first element ( $a_{1}$ ) of a geometic progression if $r = 3 and a_{4} = 324$ .	1
10865	Find $a_{5}$ of a geometric progression if $a_{1} = 5 and r = - 5$ .	1
10866	Find $a_{4}$ of a geometric progression if $a_{1} = 372 and r = \frac{1}{4}$ .	1
10867	Find $a_{4}$ of a geometric progression if $a_{1} = - 4 and r = - 8$ .	1
10868	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{23}{100} and r = 3$ .	1
10869	Find $a_{5}$ of a geometric progression if $a_{1} = - 3 and r = - 6$ .	1
10870	Find $a_{4}$ of a geometric progression if $a_{1} = - 5 and r = - 1$ .	1
10871	Find $a_{5}$ of a geometric progression if $a_{1} = 4 and r = 8$ .	1
10872	Find $a_{4}$ of a geometric progression if $a_{1} = 3 and r = - 8$ .	1
10873	Find $a_{4}$ of a geometric progression if $a_{1} = 3 and r = - 5$ .	1
10874	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{2}{77} and r = \frac{2}{77}$ .	1
10875	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{2}{77} and r = \frac{2}{77}$ .	1
10876	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{5}{6} and r = 2$ .	1
10877	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{5}{6} and r = \frac{5}{2}$ .	1
10878	Find $a_{3}$ of a geometric progression if $a_{1} = 16 and r = \frac{4}{3}$ .	1
10879	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 3 and a_{5} = \frac{3}{64}$ .	1
10880	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{4} = \frac{112}{5} and a_{8} = \frac{243}{10}$ .	1
10881	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 8 and r = \frac{1}{2}$ .	1
10882	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1024 and r = \frac{1}{2}$ .	1
10883	Find $a_{4}$ of a geometric progression if $a_{1} = - 9 and r = \frac{2}{3}$ .	1
10884	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = 54 and r = - 3$ .	1
10885	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{3}{2} and r = - \frac{1}{4}$ .	1
10886	$a_{1} = 4, r = \frac{1}{5}, a_{n} = 2, n = ?$	1
10887	Find $a_{4}$ of a geometric progression if $a_{1} = 4 and r = \frac{1}{5}$ .	1
10888	Find $a_{1} 0$ of a geometric progression if $a_{1} = \frac{5}{2} and r = - 2$ .	1
10889	Find $a_{7}$ of a geometric progression if $a_{1} = 0 and r = 3$ .	1
10890	Find $a_{7}$ of a geometric progression if $a_{1} = 153 and r = 5$ .	1
10891	Find first element ( $a_{1}$ ) of a geometic progression if $r = 3 and a_{4} = 162$ .	1
10892	Find first element ( $a_{1}$ ) of a geometic progression if $r = \frac{3}{2} and a_{3} = 270$ .	1
10893	Find $a_{7}$ of a geometric progression if $a_{1} = 120 and r = \frac{3}{2}$ .	1
10894	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1000 and r = 1.384$ .	1
10895	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 3 and r = \frac{3}{2}$ .	1
10896	$a_{1} = 4, r = \frac{1}{2}, a_{n} = \frac{1}{16}, n = ?$	1
10897	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 5 and r = \frac{1}{3}$ .	1
10898	$a_{1} = 2, r = 2, a_{n} = 512, n = ?$	1
10899	Find the sum of the first $48$ terms of a geometric sequence if $a_{1} = 3657 and r = 6.9$ .	1
10900	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{1}{2}$ .	1