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
11151	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 100 and r = 1.034$ .	1
11152	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{2}$ .	1
11153	Find first element ( $a_{1}$ ) of a geometic progression if $r = \frac{1}{2} and a_{10} = 3$ .	1
11154	Find first element ( $a_{1}$ ) of a geometic progression if $r = \frac{1}{2} and a_{7} = 24$ .	1
11155	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{7} = 24 and a_{10} = 3$ .	1
11156	Find $a_{1}$ of a geometric progression if $a_{1} = 800 and r = \frac{1}{2}$ .	1
11157	Find the sum of the first $13$ terms of a geometric sequence if $a_{1} = 190 and r = 0.9$ .	1
11158	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 247000 and r = 1.16$ .	1
11159	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = - 2 and r = - \frac{2}{5}$ .	1
11160	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 7 and r = \frac{1}{2}$ .	1
11161	Find $a_{5}$ of a geometric progression if $a_{1} = - 96 and r = - \frac{1}{2}$ .	1
11162	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 5 and r = \frac{1}{2}$ .	1
11163	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 7 and r = \frac{1}{3}$ .	1
11164	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 2 and r = 1$ .	1
11165	Find the sum of the first $25$ terms of a geometric sequence if $a_{1} = 5 and r = 2$ .	1
11166	$a_{1} = 27, r = \frac{2}{3}, a_{n} = \frac{32}{9}, n = ?$	1
11167	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = \frac{125}{216} and r = \frac{5}{6}$ .	1
11168	Find $a_{2} 0$ of a geometric progression if $a_{1} = \frac{125}{216} and r = \frac{5}{6}$ .	1
11169	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{125}{216} and r = \frac{5}{6}$ .	1
11170	$a_{1} = 5, r = \frac{13}{2}, S_{n} = 46500, n = ?$	1
11171	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 7 and r = 3$ .	1
11172	Find $a_{7}$ of a geometric progression if $a_{1} = 2 and r = \frac{1}{2}$ .	1
11173	$a_{1} = 28, r = 2.7, a_{1} = ?, r = ?$	1
11174	Find $a_{6}$ of a geometric progression if $a_{1} = 2 and r = \frac{36}{5}$ .	1
11175	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 36 and a_{3} = \frac{162}{5}$ .	1
11176	Find $a_{1} 0$ of a geometric progression if $a_{1} = 40 and r = \frac{9}{10}$ .	1
11177	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 40 and r = \frac{9}{10}$ .	1
11178	Find $a_{1} 0$ of a geometric progression if $a_{1} = 10 and r = \frac{1}{2}$ .	1
11179	Find $a_{1} 8$ of a geometric progression if $a_{1} = 10 and r = \frac{1}{2}$ .	1
11180	Find $a_{1} 7$ of a geometric progression if $a_{1} = 10 and r = \frac{1}{2}$ .	1
11181	Find $a_{8}$ of a geometric progression if $a_{1} = - \frac{1}{2} and r = 2$ .	1
11182	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 6 and r = - 4$ .	1
11183	Find $a_{3}$ of a geometric progression if $a_{1} = - 5 and r = 2$ .	1
11184	Find $a_{3}$ of a geometric progression if $a_{1} = 2 and r = 7$ .	1
11185	Find $a_{3}$ of a geometric progression if $a_{1} = 256 and r = \frac{1}{8}$ .	1
11186	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 15 and r = 11$ .	1
11187	Find $a_{1}$ of a geometric progression if $a_{1} = - \frac{1}{9} and r = \frac{1}{3}$ .	1
11188	Find $a_{7}$ of a geometric progression if $a_{1} = \frac{5}{3} and r = \frac{1}{5}$ .	1
11189	Find $a_{4} 6875$ of a geometric progression if $a_{1} = 3 and r = - 5$ .	1
11190	Find $a_{1} 0$ of a geometric progression if $a_{1} = 10000 and r = \frac{11}{10}$ .	1
11191	Find $a_{5}$ of a geometric progression if $a_{1} = 10000 and r = \frac{3}{2}$ .	1
11192	Find $a_{8}$ of a geometric progression if $a_{1} = 15 and r = 5$ .	1
11193	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = - 5 and r = \frac{1}{2}$ .	1
11194	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = - 4 and r = - 5$ .	1
11195	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1875 and r = \frac{2}{5}$ .	1
11196	Find $a_{3}$ of a geometric progression if $a_{1} = 3200 and r = \frac{1}{4}$ .	1
11197	Find $a_{8}$ of a geometric progression if $a_{1} = 3200 and r = \frac{1}{4}$ .	1
11198	Find $a_{1} 3$ of a geometric progression if $a_{1} = 6 and r = - 6$ .	1
11199	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 64 and r = \frac{3}{4}$ .	1
11200	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 30 and r = \frac{1}{2}$ .	1