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
9351	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 0.00075 and r = \frac{13}{10}$ .	1
9352	Find $a_{2} 0$ of a geometric progression if $a_{1} = \frac{1}{50} and r = - 2$ .	1
9353	Find $a_{9}$ of a geometric progression if $a_{1} = 0.02 and r = - 2$ .	1
9354	Find $a_{4}$ of a geometric progression if $a_{1} = 0.02 and r = - 2$ .	1
9355	Find $a_{1} 5$ of a geometric progression if $a_{1} = 0.02 and r = - 3$ .	1
9356	Find $a_{1} 2$ of a geometric progression if $a_{1} = 0.02 and r = - 3$ .	1
9357	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 2 and r = - \frac{1}{2}$ .	1
9358	Find $a_{8}$ of a geometric progression if $a_{1} = 6 and r = \frac{1}{3}$ .	1
9359	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 32 and r = \frac{5}{4}$ .	1
9360	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = - 2 and r = - 1$ .	1
9361	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = - 4 and r = - 3$ .	1
9362	Find $a_{3}$ of a geometric progression if $a_{1} = 18000 and r = 0.15$ .	1
9363	Find the sum of the first $11$ terms of a geometric sequence if $a_{1} = 1024 and r = - \frac{1}{2}$ .	1
9364	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 64 and r = - \frac{1}{2}$ .	1
9365	Find $a_{1}$ of a geometric progression if $a_{1} = 36 and r = \frac{1}{3}$ .	1
9366	Find $a_{1} 1$ of a geometric progression if $a_{1} = 3 and r = 12$ .	1
9367	Find $a_{1} 1$ of a geometric progression if $a_{1} = 12 and r = 3$ .	1
9368	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 7 and r = - 12$ .	1
9369	Find $a_{1} 0$ of a geometric progression if $a_{1} = \frac{33}{5} and r = - 5$ .	1
9370	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 25 and r = \frac{3}{5}$ .	1
9371	$a_{1} = 27, r = \frac{1}{3}, a_{n} = \frac{1}{729}, n = ?$	1
9372	Find $a_{9}$ of a geometric progression if $a_{1} = 256 and r = \frac{3}{2}$ .	1
9373	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 256 and r = \frac{3}{2}$ .	1
9374	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 729 and r = \frac{2}{3}$ .	1
9375	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{5} = 32 and a_{10} = 1024$ .	1
9376	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{5} = 26 and a_{13} = 4096$ .	1
9377	$a_{1} = 2.072, r = 1.882, a_{n} = 7, n = ?$	1
9378	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 2.072 and a_{13} = 4096$ .	1
9379	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 1 and r = 10$ .	1
9380	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = \frac{1}{2} and r = 10$ .	1
9381	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 9 and r = 5$ .	1
9382	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{1}{5} and r = \frac{1}{2}$ .	1
9383	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{1}{5} and r = \frac{1}{2}$ .	1
9384	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 9 and r = - \frac{2}{3}$ .	1
9385	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 60 and r = \frac{9}{10}$ .	1
9386	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{3}{2}$ .	1
9387	Find $a_{7}$ of a geometric progression if $a_{1} = \frac{1}{9} and r = - 3$ .	1
9388	Find $a_{2} 6$ of a geometric progression if $a_{1} = \frac{1}{50} and r = 2$ .	1
9389	Find $a_{5}$ of a geometric progression if $a_{1} = 3 and r = \frac{4}{3}$ .	1
9390	Find $a_{1} 2$ of a geometric progression if $a_{1} = 7 and r = - 0.3333$ .	1
9391	Find $a_{1} 2$ of a geometric progression if $a_{1} = \frac{1}{8} and r = \frac{3}{4}$ .	1
9392	Find $a_{1} 0$ of a geometric progression if $a_{1} = \frac{1}{10} and r = \frac{3}{2}$ .	1
9393	$a_{1} = 2, r = - 3, a_{1} = ?, r = ?$	1
9394	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{11}{100} and r = \frac{19}{2}$ .	1
9395	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 18 and a_{3} = 54$ .	1
9396	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = \frac{1}{9} and r = 3$ .	1
9397	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 1 and r = 3$ .	1
9398	Find $a_{1}$ of a geometric progression if $a_{1} = 3 and r = \frac{3}{7}$ .	1
9399	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 250 and r = - \frac{3}{5}$ .	1
9400	Find $a_{5}$ of a geometric progression if $a_{1} = 18 and r = \frac{5}{9}$ .	1