Geometric sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Geometric sequences.

Select category

ID	Problem	Count
351	Find $a_{1} 5$ of a geometric progression if $a_{1} = 10000 and r = 1.1$ .	10
352	Find $a_{1} 5$ of a geometric progression if $a_{1} = 30000 and r = 1.1$ .	10
353	Find $a_{6}$ of a geometric progression if $a_{1} = \frac{1}{10} and r = 9$ .	10
354	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 4 and r = - 3$ .	10
355	Find $a_{8}$ of a geometric progression if $a_{1} = - 4 and r = 4$ .	10
356	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 9 and r = - 3$ .	10
357	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 4 and r = - 2$ .	10
358	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = - 3 and r = 2$ .	10
359	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{1}{2}$ .	10
360	Find $a_{1} 0$ of a geometric progression if $a_{1} = 9 and r = - 2$ .	10
361	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 5 and r = 2$ .	10
362	Find $a_{5}$ of a geometric progression if $a_{1} = 1 and r = 6$ .	10
363	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 1 and r = 2$ .	10
364	Find $a_{6}$ of a geometric progression if $a_{1} = 800 and r = \frac{1}{2}$ .	10
365	Find $a_{1} 5$ of a geometric progression if $a_{1} = 4 and r = 2$ .	10
366	Find $a_{1} 0$ of a geometric progression if $a_{1} = 8 and r = - 4$ .	10
367	Find $a_{7}$ of a geometric progression if $a_{1} = \frac{2}{5} and r = \frac{5}{3}$ .	10
368	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = \frac{1}{100} and r = 2$ .	10
369	Find $a_{8}$ of a geometric progression if $a_{1} = 8 and r = 2$ .	10
370	Find $a_{9}$ of a geometric progression if $a_{1} = 9 and r = - 2$ .	10
371	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 5 and r = 5$ .	10
372	Find $a_{1} 0$ of a geometric progression if $a_{1} = 2 and r = - 2$ .	10
373	Find $a_{9}$ of a geometric progression if $a_{1} = - 65536 and r = - \frac{1}{4}$ .	10
374	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{2}$ .	10
375	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 10 and r = 1.22$ .	10
376	Find $a_{7}$ of a geometric progression if $a_{1} = 2 and r = 3$ .	10
377	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{3}{4}$ .	10
378	Find $a_{4}$ of a geometric progression if $a_{1} = 1 and r = 6$ .	10
379	Find $a_{7}$ of a geometric progression if $a_{1} = 4 and r = \frac{1}{3}$ .	10
380	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 100 and r = \frac{1}{100}$ .	10
381	Find $a_{8}$ of a geometric progression if $a_{1} = 0 and r = 3$ .	10
382	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 512 and r = \frac{1}{2}$ .	10
383	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{5}{2} and r = - 2$ .	10
384	Find $a_{1} 0$ of a geometric progression if $a_{1} = 6 and r = \frac{2}{3}$ .	10
385	Find $a_{1} 1$ of a geometric progression if $a_{1} = 3 and r = 2$ .	10
386	Find $a_{8}$ of a geometric progression if $a_{1} = 4 and r = - 5$ .	10
387	Find $a_{1} 0$ of a geometric progression if $a_{1} = 81 and r = \frac{1}{3}$ .	10
388	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 30 and r = - \frac{1}{5}$ .	10
389	Find $a_{1} 2$ of a geometric progression if $a_{1} = 2 and r = - 5$ .	10
390	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1 and r = - 3$ .	10
391	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = - 8 and r = - \frac{1}{4}$ .	10
392	Find the sum of the first $17$ terms of a geometric sequence if $a_{1} = 486 and r = \frac{1}{3}$ .	10
393	Find $a_{1} 0$ of a geometric progression if $a_{1} = 2 and r = 5$ .	10
394	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = - 4 and r = - 2$ .	10
395	Find $a_{1} 2$ of a geometric progression if $a_{1} = 10 and r = - 2$ .	10
396	Find $a_{1} 1$ of a geometric progression if $a_{1} = 7 and r = - 4$ .	10
397	Find $a_{7}$ of a geometric progression if $a_{1} = \frac{2}{9} and r = 3$ .	10
398	Find $a_{9}$ of a geometric progression if $a_{1} = 5 and r = 2$ .	10
399	Find $a_{3}$ of a geometric progression if $a_{1} = 5 and r = 3$ .	10
400	Find $a_{1} 3$ of a geometric progression if $a_{1} = 1 and r = 2$ .	10