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
201	Find $a_{9}$ of a geometric progression if $a_{1} = 3 and r = 4$ .	13
202	Find $a_{9}$ of a geometric progression if $a_{1} = - 8 and r = - \frac{1}{4}$ .	13
203	Find $a_{1} 1$ of a geometric progression if $a_{1} = 1 and r = - 2$ .	12
204	Find $a_{8}$ of a geometric progression if $a_{1} = 10 and r = \frac{1}{2}$ .	12
205	Find $a_{6}$ of a geometric progression if $a_{1} = 2 and r = 5$ .	12
206	Find $a_{7}$ of a geometric progression if $a_{1} = 2 and r = \frac{3}{2}$ .	12
207	Find $a_{1} 0$ of a geometric progression if $a_{1} = 5 and r = 3$ .	12
208	Find $a_{8}$ of a geometric progression if $a_{1} = 7 and r = 4$ .	12
209	Find $a_{5}$ of a geometric progression if $a_{1} = 24 and r = - \frac{1}{2}$ .	12
210	Find $a_{8}$ of a geometric progression if $a_{1} = - 3 and r = 2$ .	12
211	Find $a_{6}$ of a geometric progression if $a_{1} = 1 and r = 5$ .	12
212	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = \frac{1}{100} and r = 2$ .	12
213	Find $a_{1} 0$ of a geometric progression if $a_{1} = 18 and r = 4$ .	12
214	Find $a_{1} 2$ of a geometric progression if $a_{1} = 7 and r = - 3$ .	12
215	Find $a_{8}$ of a geometric progression if $a_{1} = 2 and r = \frac{1}{3}$ .	12
216	Find $a_{9}$ of a geometric progression if $a_{1} = 1536 and r = \frac{1}{2}$ .	12
217	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 2 and r = 3$ .	12
218	Find $a_{5}$ of a geometric progression if $a_{1} = 1 and r = - 2$ .	12
219	Find $a_{9}$ of a geometric progression if $a_{1} = 3 and r = 3$ .	12
220	$a_{1} = \frac{3}{2}, r = 2, a_{n} = 1536, n = ?$	12
221	Find $a_{1} 2$ of a geometric progression if $a_{1} = 2 and r = - 4$ .	12
222	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = 1 and r = 2$ .	12
223	Find $a_{1} 4$ of a geometric progression if $a_{1} = 10 and r = 4$ .	12
224	Find $a_{6}$ of a geometric progression if $a_{1} = - 1 and r = - 4$ .	12
225	Find $a_{5}$ of a geometric progression if $a_{1} = 5 and r = - 3$ .	12
226	Find $a_{9}$ of a geometric progression if $a_{1} = 20 and r = \frac{1}{2}$ .	12
227	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1 and r = 3$ .	12
228	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 5 and r = 3$ .	12
229	Find $a_{9}$ of a geometric progression if $a_{1} = 4 and r = - 4$ .	12
230	Find $a_{3} 0$ of a geometric progression if $a_{1} = 1 and r = \frac{1}{2}$ .	12
231	Find $a_{1} 2$ of a geometric progression if $a_{1} = 1 and r = - 2$ .	12
232	Find the sum of the first $13$ terms of a geometric sequence if $a_{1} = 3 and r = 2$ .	12
233	Find $a_{4}$ of a geometric progression if $a_{1} = 3 and r = 3$ .	12
234	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 32 and r = \frac{3}{2}$ .	12
235	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{3}{2}$ .	12
236	Find $a_{1} 2$ of a geometric progression if $a_{1} = 2 and r = - 2$ .	11
237	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 10 and r = \frac{1}{2}$ .	11
238	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 3 and r = - 2$ .	11
239	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 18 and r = \frac{1}{6}$ .	11
240	Find $a_{8}$ of a geometric progression if $a_{1} = 50 and r = 1.5$ .	11
241	Find $a_{8}$ of a geometric progression if $a_{1} = - 2 and r = - 4$ .	11
242	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 2 and r = 4$ .	11
243	Find $a_{1} 3$ of a geometric progression if $a_{1} = 4 and r = - 2$ .	11
244	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 120 and r = - \frac{2}{3}$ .	11
245	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 2 and r = 5$ .	11
246	Find $a_{8}$ of a geometric progression if $a_{1} = 1 and r = \frac{1}{2}$ .	11
247	Find $a_{6}$ of a geometric progression if $a_{1} = 4 and r = 2$ .	11
248	Find the sum of the first $64$ terms of a geometric sequence if $a_{1} = 1 and r = 2$ .	11
249	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = 1 and r = 2$ .	11
250	Find $a_{4}$ of a geometric progression if $a_{1} = 6 and r = 2$ .	11