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
1601	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 10 ~~ \text{and} ~~ a_{ 6 } = 270 $.	5
1602	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 6 } ~~ \text{and} ~~ r = \dfrac{ 25 }{ 36 } $.	5
1603	Find $ a_8 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	5
1604	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 352 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	5
1605	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 352 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	5
1606	Find $ a_130 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = \dfrac{ 49 }{ 50 } $.	5
1607	Find $ a_5 $ of a geometric progression if $ a_1 = 22 ~~ \text{and} ~~ r = 1.1 $.	5
1608	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	5
1609	Find $ a_5 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	5
1610	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $.	5
1611	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	5
1612	Find $ a_2 $ of a geometric progression if $ a_1 = 27500 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	5
1613	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	5
1614	Find $ a_5 $ of a geometric progression if $ a_1 = 1024 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	5
1615	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = 5 $.	5
1616	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 6 } = 8192 ~~ \text{and} ~~ a_{ 3 } = 85536 $.	5
1617	Find $ a_6 $ of a geometric progression if $ a_1 = 42000 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 100 } $.	5
1618	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 4 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	5
1619	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 10 }{ 3 } $.	5
1620	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 3 $.	5
1621	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 3 $.	5
1622	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $.	5
1623	Find $ a_14 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -2 $.	5
1624	Find $ a_6 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 5 $.	5
1625	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	5
1626	Find $ a_9 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	5
1627	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 125 }{ 3 } ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $.	5
1628	Find $ a_14 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = 5 $.	5
1629	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 4 $.	5
1630	Find $ a_3 $ of a geometric progression if $ a_1 = 320000 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 2 } $.	5
1631	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.41 $.	5
1632	Find $ a_6 $ of a geometric progression if $ a_1 = -20 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	5
1633	Find $ a_13 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 5 $.	5
1634	Find $ a_5 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 5 $.	5
1635	Find $ a_10 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 5 $.	5
1636	Find $ a_6 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 7 $.	5
1637	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 83 ~~ \text{and} ~~ r = -\frac{ 1 }{ 7 } $.	5
1638	Find $ a_4 $ of a geometric progression if $ a_1 = 46000 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 100 } $.	5
1639	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 60000 ~~ \text{and} ~~ r = 0.1 $.	5
1640	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = -\frac{ 3 }{ 5 } $.	5
1641	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 625 ~~ \text{and} ~~ r = 5 $.	5
1642	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = -5 $.	5
1643	Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	5
1644	$$ a_1 = 10 ~,~ r = \frac{ 5 }{ 2 } ~,~ a_n = 7 ~,~ n = ? $$	5
1645	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	5
1646	Find $ a_5 $ of a geometric progression if $ a_1 = 212 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1647	Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -5 $.	5
1648	Find $ a_5 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	5
1649	Find $ a_5 $ of a geometric progression if $ a_1 = 1024 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 8 } $.	5
1650	Find the sum of the first $ 48000 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	5