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
301	Find $a_{8}$ of a geometric progression if $a_{1} = - 4 and r = 4$ .	10
302	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 6 and r = 3$ .	10
303	Find $a_{1} 2$ of a geometric progression if $a_{1} = 4 and r = 3$ .	10
304	Find $a_{7}$ of a geometric progression if $a_{1} = - 4 and r = - 5$ .	10
305	Find $a_{1} 0$ of a geometric progression if $a_{1} = 72 and r = \frac{2}{3}$ .	10
306	$a_{1} = 10, r = \frac{11}{50}, S_{n} = 360, n = ?$	10
307	Find $a_{5}$ of a geometric progression if $a_{1} = 4 and r = \frac{3}{2}$ .	10
308	Find $a_{1} 0$ of a geometric progression if $a_{1} = 81 and r = \frac{1}{3}$ .	10
309	Find $a_{1} 2$ of a geometric progression if $a_{1} = 2 and r = - 5$ .	10
310	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = - 8 and r = - \frac{1}{4}$ .	10
311	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = 1 and r = 1$ .	10
312	Find $a_{5}$ of a geometric progression if $a_{1} = 578 and r = 7$ .	10
313	Find $a_{1} 0$ of a geometric progression if $a_{1} = 4 and r = 3$ .	10
314	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 1 and r = 2$ .	10
315	Find $a_{8}$ of a geometric progression if $a_{1} = - 3 and r = 3$ .	10
316	Find $a_{8}$ of a geometric progression if $a_{1} = 1 and r = 3$ .	10
317	Find $a_{1} 5$ of a geometric progression if $a_{1} = 4 and r = 2$ .	10
318	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = \frac{1}{100} and r = 2$ .	10
319	Find $a_{1} 0$ of a geometric progression if $a_{1} = 8 and r = - 4$ .	10
320	Find $a_{7}$ of a geometric progression if $a_{1} = \frac{2}{5} and r = \frac{5}{3}$ .	10
321	Find $a_{8}$ of a geometric progression if $a_{1} = 8 and r = 2$ .	10
322	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 5 and r = 5$ .	10
323	Find $a_{1} 0$ of a geometric progression if $a_{1} = 2 and r = - 2$ .	10
324	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{2}$ .	10
325	Find $a_{7}$ of a geometric progression if $a_{1} = 2 and r = 3$ .	10
326	Find $a_{1} 2$ of a geometric progression if $a_{1} = 8 and r = 2$ .	10
327	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 10 and r = 1.22$ .	10
328	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 4 and r = 2$ .	10
329	Find $a_{7}$ of a geometric progression if $a_{1} = - 1 and r = - 2$ .	10
330	Find $a_{4}$ of a geometric progression if $a_{1} = 1 and r = 6$ .	10
331	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = - 4 and r = - 2$ .	10
332	Find $a_{1} 0$ of a geometric progression if $a_{1} = 5 and r = 5$ .	10
333	Find $a_{1} 3$ of a geometric progression if $a_{1} = 1 and r = 2$ .	10
334	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 3 and r = 2$ .	10
335	Find $a_{4}$ of a geometric progression if $a_{1} = 4 and r = 2$ .	10
336	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{4} = 4000 and a_{8} = 49000$ .	10
337	Find $a_{4}$ of a geometric progression if $a_{1} = 5 and r = 6$ .	10
338	Find $a_{6}$ of a geometric progression if $a_{1} = \frac{1}{4} and r = - 2$ .	10
339	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 3 and r = 2$ .	10
340	Find $a_{1} 1$ of a geometric progression if $a_{1} = 1 and r = 4$ .	9
341	Find $a_{6}$ of a geometric progression if $a_{1} = 1 and r = 4$ .	9
342	Find $a_{4}$ of a geometric progression if $a_{1} = 30 and r = \frac{1}{2}$ .	9
343	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = \frac{1}{4} and r = \frac{7}{3}$ .	9
344	Find $a_{1} 1$ of a geometric progression if $a_{1} = 7 and r = 5$ .	9
345	Find $a_{1} 2$ of a geometric progression if $a_{1} = 10 and r = - 2$ .	9
346	Find $a_{1} 5$ of a geometric progression if $a_{1} = 10 and r = 2$ .	9
347	Find $a_{1} 5$ of a geometric progression if $a_{1} = 9 and r = 2$ .	9
348	Find $a_{7}$ of a geometric progression if $a_{1} = 4 and r = 2$ .	9
349	Find the sum of the first $25$ terms of a geometric sequence if $a_{1} = 1 and r = 2$ .	9
350	Find $a_{7}$ of a geometric progression if $a_{1} = 27 and r = \frac{1}{3}$ .	9