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
1651	Find $ a_4 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -5 $.	5
1652	Find $ a_10 $ of a geometric progression if $ a_1 = -9 ~~ \text{and} ~~ r = -3 $.	5
1653	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	5
1654	Find $ a_7 $ of a geometric progression if $ a_1 = 243 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 10 } $.	5
1655	Find $ a_23 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 10 } ~~ \text{and} ~~ r = 2 $.	5
1656	Find $ a_12 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 2 $.	5
1657	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	5
1658	Find $ a_5 $ of a geometric progression if $ a_1 = 700000 ~~ \text{and} ~~ r = 15 $.	5
1659	Find $ a_8 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 6 } $.	5
1660	Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 5 $.	5
1661	Find $ a_3 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	5
1662	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	5
1663	Find $ a_5 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	5
1664	Find $ a_50 $ of a geometric progression if $ a_1 = 65536 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	5
1665	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 36 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	5
1666	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 33 }{ 100 } $.	5
1667	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	5
1668	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	5
1669	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 9 $.	5
1670	Find $ a_9 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -4 $.	5
1671	Find $ a_9 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -3 $.	5
1672	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 125 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	5
1673	$$ a_1 = 36 ~,~ r = \frac{ 3 }{ 2 } ~,~ a_n = 29 ~,~ n = ? $$	5
1674	Find $ a_10 $ of a geometric progression if $ a_1 = 72 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	5
1675	Find $ a_4 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 1 $.	5
1676	Find $ a_10 $ of a geometric progression if $ a_1 = -118096 ~~ \text{and} ~~ r = -3 $.	5
1677	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.5 $.	5
1678	Find $ a_5 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 19 } $.	5
1679	Find $ a_4 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 5 $.	5
1680	Find $ a_9 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 1.02 $.	4
1681	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	4
1682	Find $ a_256 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	4
1683	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = -2 $.	4
1684	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	4
1685	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	4
1686	Find $ a_8 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	4
1687	Find $ a_6 $ of a geometric progression if $ a_1 = 1782 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	4
1688	Find $ a_5 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	4
1689	Find $ a_5 $ of a geometric progression if $ a_1 = 225 ~~ \text{and} ~~ r = 29 $.	4
1690	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 225 ~~ \text{and} ~~ r = 29 $.	4
1691	Find $ a_4 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = \dfrac{ 33 }{ 100 } $.	4
1692	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	4
1693	Find $ a_9 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -2 $.	4
1694	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = -\frac{ 4 }{ 3 } $.	4
1695	Find $ a_5 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 6 $.	4
1696	Find $ a_5 $ of a geometric progression if $ a_1 = 600 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	4
1697	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	4
1698	$$ a_1 = 20 ~,~ r = 3 ~,~ a_n = 660 ~,~ n = ? $$	4
1699	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 4 }{ 7 } ~~ \text{and} ~~ r = \dfrac{ 7 }{ 4 } $.	4
1700	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	4