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
1751	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 16 ~~ \text{and} ~~ a_{ 6 } = 250 $.	4
1752	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	4
1753	Find $ a_7 $ of a geometric progression if $ a_1 = 216 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 6 } $.	4
1754	Find $ a_29999877777777734 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -1 $.	4
1755	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 12 }{ 5 } ~~ \text{and} ~~ r = \frac{ 22 }{ 5 } $.	4
1756	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $.	4
1757	Find $ a_4 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 2 $.	4
1758	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 120 ~~ \text{and} ~~ r = 1.1 $.	4
1759	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	4
1760	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -2 $.	4
1761	Find $ a_2 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	4
1762	Find $ a_2 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	4
1763	Find $ a_12 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	4
1764	Find $ a_12 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	4
1765	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	4
1766	Find $ a_3 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = -\dfrac{ 4 }{ 3 } $.	4
1767	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	4
1768	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 10 } ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	4
1769	Find $ a_3 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 9 $.	4
1770	Find $ a_13 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	4
1771	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	4
1772	Find the sum of the first $ 36 $ terms of a geometric sequence if $ a_1 = 256 ~~ \text{and} ~~ r = 1.1 $.	4
1773	$$ a_1 = 256 ~,~ r = 1.2 ~,~ S_n = 4200000 ~,~ n = ? $$	4
1774	Find $ a_6 $ of a geometric progression if $ a_1 = 256 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	4
1775	Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 50 $.	4
1776	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 16 $.	4
1777	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -\frac{ 4 }{ 3 } $.	4
1778	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	4
1779	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	4
1780	Find $ a_8 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -4 $.	4
1781	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 6 $.	4
1782	Find $ a_20 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	4
1783	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -5 $.	4
1784	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 54 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	4
1785	Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -2 $.	4
1786	Find $ a_7 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	4
1787	Find $ a_12 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -5 $.	4
1788	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -4 $.	4
1789	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	4
1790	Find $ a_30 $ of a geometric progression if $ a_1 = 0.01 ~~ \text{and} ~~ r = 2 $.	4
1791	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	4
1792	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	4
1793	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 20 } ~~ \text{and} ~~ r = \frac{ 17 }{ 20 } $.	4
1794	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 0.15 ~~ \text{and} ~~ r = 0.85 $.	4
1795	Find $ a_10 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = 3 $.	4
1796	Find $ a_45 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	4
1797	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 6 } $.	4
1798	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	4
1799	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	4
1800	Find $ a_151 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -2 $.	4