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
1551	Find $ a_6 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	5
1552	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 6 ~~ \text{and} ~~ a_{ 4 } = 1295 $.	5
1553	Find $ a_9 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -4 $.	5
1554	Find $ a_9 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -5 $.	5
1555	Find $ a_10 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	5
1556	Find $ a_6 $ of a geometric progression if $ a_1 = 23 ~~ \text{and} ~~ r = 4 $.	5
1557	Find $ a_10 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	5
1558	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	5
1559	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 10 $.	5
1560	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	5
1561	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	5
1562	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1.688 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	5
1563	Find $ a_31 $ of a geometric progression if $ a_1 = 0.01 ~~ \text{and} ~~ r = 2 $.	5
1564	Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	5
1565	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	5
1566	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	5
1567	Find $ a_8 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -2 $.	5
1568	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1569	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	5
1570	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = -3 $.	5
1571	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 0.2 $.	5
1572	Find $ a_10 $ of a geometric progression if $ a_1 = 11 ~~ \text{and} ~~ r = 3 $.	5
1573	Find $ a_12 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	5
1574	Find $ a_9 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 5 $.	5
1575	Find $ a_13 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $.	5
1576	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 0.005 ~~ \text{and} ~~ r = 1.2 $.	5
1577	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 0.005 ~~ \text{and} ~~ r = 1.2 $.	5
1578	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 0.005 ~~ \text{and} ~~ r = 1.1 $.	5
1579	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 16 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 25 } $.	5
1580	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	5
1581	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	5
1582	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 7 }{ 12 } ~~ \text{and} ~~ r = \frac{ 7 }{ 3 } $.	5
1583	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1584	Find $ a_9 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	5
1585	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ r = 0.7753 $.	5
1586	$$ a_1 = 1 ~,~ r = 5 ~,~ S_n = 3906 ~,~ n = ? $$	5
1587	Find $ a_4 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 10 $.	5
1588	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	5
1589	Find $ a_5 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -3 $.	5
1590	Find $ a_5 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 10 $.	5
1591	Find $ a_1095 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 0.5 $.	5
1592	Find $ a_1095 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 1.5 $.	5
1593	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	5
1594	Find $ a_9 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1595	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = -80 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	5
1596	Find $ a_12 $ of a geometric progression if $ a_1 = -\dfrac{ 3 }{ 8 } ~~ \text{and} ~~ r = 2 $.	5
1597	Find $ a_10 $ of a geometric progression if $ a_1 = 2700 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	5
1598	Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = 72 ~~ \text{and} ~~ r = -\frac{ 5 }{ 6 } $.	5
1599	Find $ a_5 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $.	5
1600	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 8 } = 21 ~~ \text{and} ~~ a_{ 27 } = 97 $.	5