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
11101	Find $a_{7}$ of a geometric progression if $a_{1} = 15 and r = 1.5$ .	1
11102	Find $a_{5}$ of a geometric progression if $a_{1} = 60 and r = - \frac{1}{2}$ .	1
11103	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 1 and r = 3$ .	1
11104	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1 and r = - 3$ .	1
11105	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{3}$ .	1
11106	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 1 and r = - \frac{1}{3}$ .	1
11107	Find $a_{3}$ of a geometric progression if $a_{1} = \frac{3}{16} and r = \frac{1}{2}$ .	1
11108	Find $a_{1} 5$ of a geometric progression if $a_{1} = \frac{3}{16} and r = \frac{1}{2}$ .	1
11109	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = \frac{3}{16} and r = \frac{1}{2}$ .	1
11110	Find $a_{4}$ of a geometric progression if $a_{1} = 320 and r = 4$ .	1
11111	Find $a_{4}$ of a geometric progression if $a_{1} = 192 and r = - 4$ .	1
11112	Find $a_{4}$ of a geometric progression if $a_{1} = - 375 and r = 5$ .	1
11113	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 200 and r = \frac{1}{2}$ .	1
11114	Find $a_{9}$ of a geometric progression if $a_{1} = 27 and r = 3$ .	1
11115	Find $a_{1} 6$ of a geometric progression if $a_{1} = 4 and r = - 3$ .	1
11116	Find $a_{1} 1$ of a geometric progression if $a_{1} = 2 and r = 3$ .	1
11117	Find $a_{9}$ of a geometric progression if $a_{1} = 3 and r = - 2$ .	1
11118	Find $a_{1} 9$ of a geometric progression if $a_{1} = 14 and r = 1.5$ .	1
11119	Find $a_{6}$ of a geometric progression if $a_{1} = 12 and r = - \frac{1}{4}$ .	1
11120	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 12 and r = - \frac{1}{4}$ .	1
11121	Find $a_{1} 0$ of a geometric progression if $a_{1} = 13 and r = 3$ .	1
11122	Find $a_{4}$ of a geometric progression if $a_{1} = 10 and r = 5$ .	1
11123	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 7 and r = 3$ .	1
11124	Find $a_{3}$ of a geometric progression if $a_{1} = 100 and r = \frac{103}{100}$ .	1
11125	Find $a_{1} 1$ of a geometric progression if $a_{1} = 256 and r = - 2$ .	1
11126	Find $a_{1} 1$ of a geometric progression if $a_{1} = 256 and r = \frac{1}{2}$ .	1
11127	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = - 3 and r = 2.4$ .	1
11128	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = \frac{5}{8} and r = - 2$ .	1
11129	Find $a_{8}$ of a geometric progression if $a_{1} = 320 and r = \frac{1}{2}$ .	1
11130	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 280 and r = \frac{3}{4}$ .	1
11131	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = \frac{56}{5} and r = \frac{8}{5}$ .	1
11132	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 43 and r = 4$ .	1
11133	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = - 192 and r = - \frac{4}{3}$ .	1
11134	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{8}{9}$ .	1
11135	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 4 and r = 3$ .	1
11136	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 2 and r = 9$ .	1
11137	Find $a_{5}$ of a geometric progression if $a_{1} = - 7 and r = 6$ .	1
11138	Find the sum of the first $40$ terms of a geometric sequence if $a_{1} = 10000 and r = 1.06$ .	1
11139	Find $a_{4} 0$ of a geometric progression if $a_{1} = 10000 and r = 1.06$ .	1
11140	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 9 and a_{3} = 144$ .	1
11141	Find $a_{7}$ of a geometric progression if $a_{1} = 100 and r = 1.06$ .	1
11142	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{3} = 9 and a_{5} = 81$ .	1
11143	Find $a_{1} 4$ of a geometric progression if $a_{1} = 10 and r = 2$ .	1
11144	Find $a_{1}$ of a geometric progression if $a_{1} = 2 and r = 2$ .	1
11145	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 18 and r = \frac{2}{3}$ .	1
11146	Find $a_{4} 3$ of a geometric progression if $a_{1} = 2 and r = 0.85$ .	1
11147	Find $a_{9}$ of a geometric progression if $a_{1} = 10000 and r = \frac{1}{10}$ .	1
11148	Find $a_{9}$ of a geometric progression if $a_{1} = 10000 and r = 0.1$ .	1
11149	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 100 and r = 1.029$ .	1
11150	Find $a_{1} 5$ of a geometric progression if $a_{1} = 4 and r = 3$ .	1