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
251	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 20 and r = \frac{1}{2}$ .	11
252	Find $a_{4}$ of a geometric progression if $a_{1} = 1 and r = 4$ .	11
253	Find $a_{5}$ of a geometric progression if $a_{1} = 1 and r = 4$ .	11
254	Find $a_{1} 0$ of a geometric progression if $a_{1} = 8 and r = - 3$ .	11
255	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 3 and r = 6$ .	11
256	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 6 and r = 2$ .	11
257	Find $a_{1} 1$ of a geometric progression if $a_{1} = 4 and r = \frac{1}{2}$ .	11
258	Find $a_{5}$ of a geometric progression if $a_{1} = - 5 and r = - 3$ .	11
259	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 2 and r = 3$ .	11
260	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{1}{2} and r = \frac{1}{2}$ .	11
261	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = 1 and r = 2$ .	11
262	Find $a_{4}$ of a geometric progression if $a_{1} = 4 and r = 6$ .	11
263	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 8 and r = \frac{3}{2}$ .	11
264	Find $a_{7}$ of a geometric progression if $a_{1} = 2 and r = - 3$ .	11
265	Find $a_{9}$ of a geometric progression if $a_{1} = 2 and r = 3$ .	11
266	Find $a_{1} 8$ of a geometric progression if $a_{1} = 10000 and r = 1.1$ .	11
267	Find $a_{1} 8$ of a geometric progression if $a_{1} = 20000 and r = 1.1$ .	11
268	Find $a_{2} 0$ of a geometric progression if $a_{1} = 20000 and r = 1.1$ .	11
269	Find $a_{1} 1$ of a geometric progression if $a_{1} = 4 and r = - 2$ .	10
270	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 2 and r = 2$ .	10
271	Find $a_{5}$ of a geometric progression if $a_{1} = 2 and r = - 3$ .	10
272	Find $a_{6}$ of a geometric progression if $a_{1} = \frac{1}{10} and r = 9$ .	10
273	Find $a_{1} 1$ of a geometric progression if $a_{1} = - 1 and r = - 2$ .	10
274	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1 and r = 9$ .	10
275	Find $a_{6}$ of a geometric progression if $a_{1} = \frac{3}{5} and r = - 5$ .	10
276	Find $a_{1} 5$ of a geometric progression if $a_{1} = 10000 and r = 1.1$ .	10
277	Find $a_{1} 5$ of a geometric progression if $a_{1} = 30000 and r = 1.1$ .	10
278	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = - 5 and r = - 3$ .	10
279	Find $a_{8}$ of a geometric progression if $a_{1} = \frac{3}{10} and r = 2$ .	10
280	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1 and r = 6$ .	10
281	Find $a_{8}$ of a geometric progression if $a_{1} = 1 and r = \frac{1}{2}$ .	10
282	Find $a_{1} 0$ of a geometric progression if $a_{1} = 6 and r = \frac{2}{3}$ .	10
283	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{5}{2} and r = - 2$ .	10
284	Find $a_{8}$ of a geometric progression if $a_{1} = 2 and r = 5$ .	10
285	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 2 and r = 2$ .	10
286	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 512 and r = \frac{1}{2}$ .	10
287	Find $a_{1} 3$ of a geometric progression if $a_{1} = 4 and r = - 4$ .	10
288	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 100 and r = \frac{1}{100}$ .	10
289	Find $a_{7}$ of a geometric progression if $a_{1} = 4 and r = \frac{1}{3}$ .	10
290	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{1}{2}$ .	10
291	Find $a_{8}$ of a geometric progression if $a_{1} = - 4 and r = 4$ .	10
292	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 6 and r = 3$ .	10
293	Find $a_{1} 2$ of a geometric progression if $a_{1} = 4 and r = 3$ .	10
294	Find $a_{7}$ of a geometric progression if $a_{1} = - 4 and r = - 5$ .	10
295	Find $a_{1} 0$ of a geometric progression if $a_{1} = 72 and r = \frac{2}{3}$ .	10
296	Find $a_{8}$ of a geometric progression if $a_{1} = - 2 and r = - 4$ .	10
297	$a_{1} = 10, r = \frac{11}{50}, S_{n} = 360, n = ?$	10
298	Find $a_{5}$ of a geometric progression if $a_{1} = 4 and r = \frac{3}{2}$ .	10
299	Find $a_{1} 0$ of a geometric progression if $a_{1} = 81 and r = \frac{1}{3}$ .	10
300	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = - 8 and r = - \frac{1}{4}$ .	10