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
9901	Find the sum of the first $1$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{27}{25}$ .	1
9902	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{27}{25}$ .	1
9903	Find the sum of the first $100$ terms of a geometric sequence if $a_{1} = 1 and r = 1.08$ .	1
9904	Find the sum of the first $100$ terms of a geometric sequence if $a_{1} = 2 and r = 2$ .	1
9905	Find the sum of the first $100$ terms of a geometric sequence if $a_{1} = 24 and r = \frac{1}{2}$ .	1
9906	Find the sum of the first $100$ terms of a geometric sequence if $a_{1} = 3 and r = 2$ .	1
9907	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 5 and r = - \frac{2}{5}$ .	1
9908	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 30 and r = - 5$ .	1
9909	Find $a_{8}$ of a geometric progression if $a_{1} = 50000 and r = 2$ .	1
9910	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 21 and r = - 5$ .	1
9911	Find $a_{4}$ of a geometric progression if $a_{1} = 50000 and r = 2$ .	1
9912	Find $a_{6}$ of a geometric progression if $a_{1} = 50000 and r = 2$ .	1
9913	Find $a_{3}$ of a geometric progression if $a_{1} = 1000 and r = 2$ .	1
9914	Find $a_{9}$ of a geometric progression if $a_{1} = 27 and r = \frac{1}{3}$ .	1
9915	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = \frac{21}{10} and r = 2$ .	1
9916	Find $a_{4}$ of a geometric progression if $a_{1} = 67 and r = 13$ .	1
9917	Find $a_{5}$ of a geometric progression if $a_{1} = 360 and r = \frac{7}{8}$ .	1
9918	Find $a_{4}$ of a geometric progression if $a_{1} = - 1 and r = - 8$ .	1
9919	Find $a_{5}$ of a geometric progression if $a_{1} = - 2 and r = - 8$ .	1
9920	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 0.5 and r = 0.5$ .	1
9921	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = \frac{1}{2} and r = \frac{1}{2}$ .	1
9922	$a_{1} = 2, r = \frac{3}{2}, a_{1} = ?, r = ?$	1
9923	Find $a_{5} 4$ of a geometric progression if $a_{1} = 1025 and r = 8$ .	1
9924	Find $a_{5} 8$ of a geometric progression if $a_{1} = 2 and r = \frac{1}{4}$ .	1
9925	Find $a_{3}$ of a geometric progression if $a_{1} = 80 and r = 8$ .	1
9926	Find $a_{3}$ of a geometric progression if $a_{1} = 80 and r = 0.9$ .	1
9927	Find $a_{4} 5$ of a geometric progression if $a_{1} = 152 and r = - 3$ .	1
9928	$a_{1} = 9, r = \frac{3}{5}, a_{n} = 8, n = ?$	1
9929	$a_{1} = 5, r = 2, a_{n} = 2560, n = ?$	1
9930	Find $a_{1}$ of a geometric progression if $a_{1} = \frac{2}{5} and r = - 1$ .	1
9931	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1 and r = 1.08$ .	1
9932	Find $a_{1} 2$ of a geometric progression if $a_{1} = \frac{2}{5} and r = 5$ .	1
9933	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 9 and r = - 3$ .	1
9934	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 2 and r = - 3$ .	1
9935	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 3 and r = - 3$ .	1
9936	Find $a_{5}$ of a geometric progression if $a_{1} = - 3 and r = 3$ .	1
9937	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{81}{25} and r = \frac{3}{5}$ .	1
9938	Find $a_{4}$ of a geometric progression if $a_{1} = 1000 and r = \frac{1}{10}$ .	1
9939	Find $a_{8}$ of a geometric progression if $a_{1} = \frac{3}{5} and r = \frac{1}{2}$ .	1
9940	Find $a_{6}$ of a geometric progression if $a_{1} = 0 and r = 0.05$ .	1
9941	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = 16 and r = - \frac{1}{4}$ .	1
9942	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = 16 and r = - \frac{1}{4}$ .	1
9943	Find common ratio ( $r$ ) in geometic progression if $a_{1} = \frac{1}{5} and a_{2} = \frac{5}{3}$ .	1
9944	Find $a_{8}$ of a geometric progression if $a_{1} = 8 and r = \frac{3}{2}$ .	1
9945	Find $a_{3}$ of a geometric progression if $a_{1} = 15 and r = \frac{2}{3}$ .	1
9946	Find $a_{1} 4$ of a geometric progression if $a_{1} = 1000 and r = \frac{1}{2}$ .	1
9947	Find $a_{3}$ of a geometric progression if $a_{1} = \frac{7}{2} and r = 3$ .	1
9948	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 3 and r = - 2$ .	1
9949	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 2 and r = 3$ .	1
9950	Find $a_{4}$ of a geometric progression if $a_{1} = 600 and r = \frac{27}{25}$ .	1