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
9501	Find $a_{1} 1$ of a geometric progression if $a_{1} = 256 and r = - 2$ .	1
9502	Find $a_{1} 1$ of a geometric progression if $a_{1} = 256 and r = \frac{1}{2}$ .	1
9503	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = - 3 and r = 2.4$ .	1
9504	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = \frac{5}{8} and r = - 2$ .	1
9505	Find $a_{8}$ of a geometric progression if $a_{1} = 320 and r = \frac{1}{2}$ .	1
9506	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 280 and r = \frac{3}{4}$ .	1
9507	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = \frac{56}{5} and r = \frac{8}{5}$ .	1
9508	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 43 and r = 4$ .	1
9509	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = - 192 and r = - \frac{4}{3}$ .	1
9510	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{8}{9}$ .	1
9511	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 4 and r = 3$ .	1
9512	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 2 and r = 9$ .	1
9513	Find $a_{5}$ of a geometric progression if $a_{1} = - 7 and r = 6$ .	1
9514	Find the sum of the first $40$ terms of a geometric sequence if $a_{1} = 10000 and r = 1.06$ .	1
9515	Find $a_{4} 0$ of a geometric progression if $a_{1} = 10000 and r = 1.06$ .	1
9516	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 9 and a_{3} = 144$ .	1
9517	Find $a_{7}$ of a geometric progression if $a_{1} = 100 and r = 1.06$ .	1
9518	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{3} = 9 and a_{5} = 81$ .	1
9519	Find $a_{1} 4$ of a geometric progression if $a_{1} = 10 and r = 2$ .	1
9520	Find $a_{1}$ of a geometric progression if $a_{1} = 2 and r = 2$ .	1
9521	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 18 and r = \frac{2}{3}$ .	1
9522	Find $a_{4} 3$ of a geometric progression if $a_{1} = 2 and r = 0.85$ .	1
9523	Find $a_{9}$ of a geometric progression if $a_{1} = 10000 and r = \frac{1}{10}$ .	1
9524	Find $a_{9}$ of a geometric progression if $a_{1} = 10000 and r = 0.1$ .	1
9525	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 100 and r = 1.029$ .	1
9526	Find $a_{1} 5$ of a geometric progression if $a_{1} = 4 and r = 3$ .	1
9527	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 100 and r = 1.034$ .	1
9528	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{2}$ .	1
9529	Find first element ( $a_{1}$ ) of a geometic progression if $r = \frac{1}{2} and a_{10} = 3$ .	1
9530	Find first element ( $a_{1}$ ) of a geometic progression if $r = \frac{1}{2} and a_{7} = 24$ .	1
9531	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{7} = 24 and a_{10} = 3$ .	1
9532	Find $a_{1}$ of a geometric progression if $a_{1} = 800 and r = \frac{1}{2}$ .	1
9533	Find the sum of the first $13$ terms of a geometric sequence if $a_{1} = 190 and r = 0.9$ .	1
9534	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 247000 and r = 1.16$ .	1
9535	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = - 2 and r = - \frac{2}{5}$ .	1
9536	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 7 and r = \frac{1}{2}$ .	1
9537	Find $a_{5}$ of a geometric progression if $a_{1} = - 96 and r = - \frac{1}{2}$ .	1
9538	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 5 and r = \frac{1}{2}$ .	1
9539	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 7 and r = \frac{1}{3}$ .	1
9540	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 2 and r = 1$ .	1
9541	Find the sum of the first $25$ terms of a geometric sequence if $a_{1} = 5 and r = 2$ .	1
9542	$a_{1} = 27, r = \frac{2}{3}, a_{n} = \frac{32}{9}, n = ?$	1
9543	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = \frac{125}{216} and r = \frac{5}{6}$ .	1
9544	Find $a_{2} 0$ of a geometric progression if $a_{1} = \frac{125}{216} and r = \frac{5}{6}$ .	1
9545	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{125}{216} and r = \frac{5}{6}$ .	1
9546	$a_{1} = 5, r = \frac{13}{2}, S_{n} = 46500, n = ?$	1
9547	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 7 and r = 3$ .	1
9548	Find $a_{7}$ of a geometric progression if $a_{1} = 2 and r = \frac{1}{2}$ .	1
9549	$a_{1} = 28, r = 2.7, a_{1} = ?, r = ?$	1
9550	Find $a_{6}$ of a geometric progression if $a_{1} = 2 and r = \frac{36}{5}$ .	1