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
9751	Find $a_{5}$ of a geometric progression if $a_{1} = 512 and r = \frac{1}{2}$ .	1
9752	Find $a_{1} 1$ of a geometric progression if $a_{1} = 3246 and r = \frac{1}{10}$ .	1
9753	Find $a_{2} 1$ of a geometric progression if $a_{1} = 4000 and r = \frac{1}{4}$ .	1
9754	Find $a_{9}$ of a geometric progression if $a_{1} = 2500 and r = 5$ .	1
9755	Find $a_{1}$ of a geometric progression if $a_{1} = 36 and r = \frac{2}{3}$ .	1
9756	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = \frac{1}{2} and r = - 5$ .	1
9757	Find $a_{1} 2$ of a geometric progression if $a_{1} = 9 and r = 1.5$ .	1
9758	Find $a_{2}$ of a geometric progression if $a_{1} = - \frac{1}{27} and r = \frac{1}{243}$ .	1
9759	Find first element ( $a_{1}$ ) of a geometic progression if $r = \frac{1}{2} and a_{2} = 8$ .	1
9760	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{3} = \frac{175}{4} and a_{4} = \frac{875}{8}$ .	1
9761	Find $a_{1} 0$ of a geometric progression if $a_{1} = 7 and r = \frac{5}{2}$ .	1
9762	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{3} = \frac{75}{16} and a_{4} = \frac{375}{64}$ .	1
9763	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 32805 and a_{2} = 3645$ .	1
9764	Find $a_{8}$ of a geometric progression if $a_{1} = 32805 and r = \frac{1}{9}$ .	1
9765	Find the sum of the first $100$ terms of a geometric sequence if $a_{1} = \frac{5}{2} and r = \frac{1}{2}$ .	1
9766	$a_{1} = 20, r = \frac{9}{10}, S_{n} = \frac{8853}{20}, n = ?$	1
9767	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = 2 and r = \frac{6}{5}$ .	1
9768	Find the sum of the first $36$ terms of a geometric sequence if $a_{1} = 480 and r = 1.01$ .	1
9769	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{1}{8} and r = 4$ .	1
9770	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 30 and r = - \frac{1}{10}$ .	1
9771	$a_{1} = 1, r = 7, a_{1} = ?, r = ?$	1
9772	$a_{1} = 8, r = 2, a_{n} = 22, n = ?$	1
9773	Find $a_{2} 2$ of a geometric progression if $a_{1} = 8 and r = 2$ .	1
9774	Find $a_{7}$ of a geometric progression if $a_{1} = 1000000000 and r = \frac{1}{10}$ .	1
9775	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 2 and r = - 2$ .	1
9776	Find $a_{7}$ of a geometric progression if $a_{1} = 12 and r = \frac{7}{20}$ .	1
9777	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 32 and r = - \frac{1}{2}$ .	1
9778	Find $a_{2} 0$ of a geometric progression if $a_{1} = 3 and r = 3$ .	1
9779	Find $a_{9}$ of a geometric progression if $a_{1} = 240 and r = \frac{1}{5}$ .	1
9780	Find $a_{2}$ of a geometric progression if $a_{1} = 5 and r = - 2$ .	1
9781	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{5}{4}$ .	1
9782	Find $a_{4}$ of a geometric progression if $a_{1} = 150 and r = 2$ .	1
9783	Find $a_{4}$ of a geometric progression if $a_{1} = 150 and r = 0.5$ .	1
9784	Find $a_{4}$ of a geometric progression if $a_{1} = 150 and r = 1.5$ .	1
9785	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 1 and r = - 1$ .	1
9786	Find $a_{9}$ of a geometric progression if $a_{1} = 5 and r = \frac{1}{3}$ .	1
9787	Find $a_{6}$ of a geometric progression if $a_{1} = 8 and r = \frac{2}{3}$ .	1
9788	Find $a_{1}$ of a geometric progression if $a_{1} = 1 and r = \frac{9}{4}$ .	1
9789	Find $a_{9}$ of a geometric progression if $a_{1} = \frac{1}{2} and r = \frac{1}{2}$ .	1
9790	Find $a_{3} 0$ of a geometric progression if $a_{1} = 5000 and r = 1.08$ .	1
9791	Find $a_{5}$ of a geometric progression if $a_{1} = 8 and r = \frac{1}{4}$ .	1
9792	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 5 and r = \frac{3}{4}$ .	1
9793	Find $a_{3} 2$ of a geometric progression if $a_{1} = 9 and r = - 1$ .	1
9794	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1500 and r = 3$ .	1
9795	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = 1512 and r = 6$ .	1
9796	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 12 and r = - 2$ .	1
9797	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = - 12 and r = - 2$ .	1
9798	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = - 4 and r = - 2$ .	1
9799	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 4 and r = - 1$ .	1
9800	Find $a_{9}$ of a geometric progression if $a_{1} = 4 and r = - 1$ .	1