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	$$ a_1 = \frac{ 3 }{ 2 } ~,~ r = 2 ~,~ a_n = 1536 ~,~ n = ? $$	12
252	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	12
253	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	12
254	Find $ a_8 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 4 $.	12
255	Find $ a_14 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 4 $.	12
256	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $.	12
257	Find $ a_30 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	12
258	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	12
259	Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	12
260	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	12
261	Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $.	12
262	Find $ a_9 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -4 $.	12
263	Find $ a_9 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	12
264	Find $ a_8 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -2 $.	12
265	Find $ a_10 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	12
266	Find $ a_7 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	12
267	Find the sum of the first $ 64 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	12
268	Find $ a_5 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	12
269	Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 5 $.	12
270	Find $ a_8 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 2 $.	12
271	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	12
272	Find $ a_9 $ of a geometric progression if $ a_1 = 1536 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	12
273	Find $ a_10 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = 4 $.	12
274	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $.	12
275	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	12
276	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	12
277	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	12
278	Find $ a_4 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	12
279	Find $ a_6 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	11
280	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	11
281	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	11
282	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	11
283	Find $ a_8 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 2 $.	11
284	Find $ a_25 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	11
285	Find $ a_12 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	11
286	Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	11
287	Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $.	11
288	Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	11
289	Find $ a_9 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	11
290	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	11
291	Find $ a_7 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -2 $.	11
292	Find $ a_7 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	11
293	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	11
294	Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 5 $.	11
295	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	11
296	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	11
297	Find $ a_8 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 1.5 $.	11
298	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = \frac{ 1 }{ 6 } $.	11
299	Find $ a_9 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -5 $.	11
300	Find $ a_8 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	11