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
9951	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = \frac{1}{2} and r = \frac{1}{2}$ .	1
9952	$a_{1} = 2, r = \frac{3}{2}, a_{1} = ?, r = ?$	1
9953	Find $a_{5} 4$ of a geometric progression if $a_{1} = 1025 and r = 8$ .	1
9954	Find $a_{5} 8$ of a geometric progression if $a_{1} = 2 and r = \frac{1}{4}$ .	1
9955	Find $a_{3}$ of a geometric progression if $a_{1} = 80 and r = 8$ .	1
9956	Find $a_{3}$ of a geometric progression if $a_{1} = 80 and r = 0.9$ .	1
9957	Find $a_{4} 5$ of a geometric progression if $a_{1} = 152 and r = - 3$ .	1
9958	$a_{1} = 9, r = \frac{3}{5}, a_{n} = 8, n = ?$	1
9959	$a_{1} = 5, r = 2, a_{n} = 2560, n = ?$	1
9960	Find $a_{1}$ of a geometric progression if $a_{1} = \frac{2}{5} and r = - 1$ .	1
9961	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1 and r = 1.08$ .	1
9962	Find $a_{1} 2$ of a geometric progression if $a_{1} = \frac{2}{5} and r = 5$ .	1
9963	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 9 and r = - 3$ .	1
9964	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 2 and r = - 3$ .	1
9965	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 3 and r = - 3$ .	1
9966	Find $a_{5}$ of a geometric progression if $a_{1} = - 3 and r = 3$ .	1
9967	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{81}{25} and r = \frac{3}{5}$ .	1
9968	Find $a_{4}$ of a geometric progression if $a_{1} = 1000 and r = \frac{1}{10}$ .	1
9969	Find $a_{8}$ of a geometric progression if $a_{1} = \frac{3}{5} and r = \frac{1}{2}$ .	1
9970	Find $a_{6}$ of a geometric progression if $a_{1} = 0 and r = 0.05$ .	1
9971	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = 16 and r = - \frac{1}{4}$ .	1
9972	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = 16 and r = - \frac{1}{4}$ .	1
9973	Find common ratio ( $r$ ) in geometic progression if $a_{1} = \frac{1}{5} and a_{2} = \frac{5}{3}$ .	1
9974	Find $a_{8}$ of a geometric progression if $a_{1} = 8 and r = \frac{3}{2}$ .	1
9975	Find $a_{3}$ of a geometric progression if $a_{1} = 15 and r = \frac{2}{3}$ .	1
9976	Find $a_{1} 4$ of a geometric progression if $a_{1} = 1000 and r = \frac{1}{2}$ .	1
9977	Find $a_{3}$ of a geometric progression if $a_{1} = \frac{7}{2} and r = 3$ .	1
9978	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 3 and r = - 2$ .	1
9979	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 2 and r = 3$ .	1
9980	Find $a_{4}$ of a geometric progression if $a_{1} = 600 and r = \frac{27}{25}$ .	1
9981	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 600 and r = \frac{27}{25}$ .	1
9982	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 20 and a_{3} = \frac{45}{4}$ .	1
9983	Find $a_{1} 6$ of a geometric progression if $a_{1} = 50000 and r = \frac{26}{25}$ .	1
9984	Find $a_{4}$ of a geometric progression if $a_{1} = 14 and r = \frac{1}{3}$ .	1
9985	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 2 and r = \frac{119}{5}$ .	1
9986	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{3}{10} and r = \frac{1}{2}$ .	1
9987	Find the sum of the first $175$ terms of a geometric sequence if $a_{1} = 515036 and r = 1.08$ .	1
9988	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{3}{10} and r = \frac{3}{5}$ .	1
9989	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = - \frac{2}{25} and r = - \frac{2}{5}$ .	1
9990	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{1}{5} and r = \frac{3}{5}$ .	1
9991	Find $a_{3} 0$ of a geometric progression if $a_{1} = 14 and r = 2$ .	1
9992	Find the sum of the first $26$ terms of a geometric sequence if $a_{1} = 1987 and r = 0.03$ .	1
9993	Find $a_{3}$ of a geometric progression if $a_{1} = 50000 and r = \frac{11}{10}$ .	1
9994	Find the sum of the first $60$ terms of a geometric sequence if $a_{1} = 10186 and r = 1.006$ .	1
9995	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 75 and r = \frac{1}{2}$ .	1
9996	Find $a_{4}$ of a geometric progression if $a_{1} = 402050 and r = \frac{51}{50}$ .	1
9997	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 3 and r = \frac{2}{3}$ .	1
9998	Find $a_{1} 2$ of a geometric progression if $a_{1} = 81 and r = - \frac{1}{3}$ .	1
9999	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{16}{9} and r = \frac{3}{2}$ .	1
10000	Find $a_{7}$ of a geometric progression if $a_{1} = 32 and r = \frac{1}{4}$ .	1