Geometric sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Geometric sequences.

Select category

ID	Problem	Count
1501	Find $ a_3 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = 6 $.	5
1502	Find $ a_11 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -2 $.	5
1503	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	5
1504	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $.	5
1505	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	5
1506	Find $ a_25 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -1 $.	5
1507	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	5
1508	Find $ a_4 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	5
1509	Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 5 $.	5
1510	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 54000 ~~ \text{and} ~~ r = 1.35 $.	5
1511	Find $ a_5 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -5 $.	5
1512	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -2 $.	5
1513	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1500 ~~ \text{and} ~~ r = 1.045 $.	5
1514	Find $ a_9 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	5
1515	Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -4 $.	5
1516	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 12 ~~ \text{and} ~~ a_{ 10 } = 26244 $.	5
1517	Find $ a_8 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 5 $.	5
1518	$$ a_1 = \frac{ 3 }{ 2 } ~~,~~ r = \frac{ 23 }{ 20 } ~~,~~ a_1 = ? ~~,~~ r = ? $$	5
1519	$$ a_1 = \frac{ 15272 }{ 25 } ~,~ r = 1.871 ~,~ a_n = 6 ~,~ n = ? $$	5
1520	Find $ a_8 $ of a geometric progression if $ a_1 = 0.25 ~~ \text{and} ~~ r = 7 $.	5
1521	Find $ a_6 $ of a geometric progression if $ a_1 = 0.25 ~~ \text{and} ~~ r = 7 $.	5
1522	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 0.25 ~~ \text{and} ~~ r = 7 $.	5
1523	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 7 $.	5
1524	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 7 $.	5
1525	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	5
1526	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = 2 $.	5
1527	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 8 $.	5
1528	Find $ a_12 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -5 $.	5
1529	Find $ a_3 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	5
1530	Find $ a_16 $ of a geometric progression if $ a_1 = 35000 ~~ \text{and} ~~ r = 6 $.	5
1531	Find $ a_6 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = 3 $.	5
1532	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	5
1533	Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	5
1534	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $.	5
1535	Find $ a_15 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.	5
1536	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 175 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	5
1537	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	5
1538	Find $ a_5 $ of a geometric progression if $ a_1 = 625 ~~ \text{and} ~~ r = 5 $.	5
1539	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $.	5
1540	Find $ a_3 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	5
1541	Find $ a_9 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	5
1542	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 0.5 $.	5
1543	Find the sum of the first $ 1336 $ terms of a geometric sequence if $ a_1 = 5.2 ~~ \text{and} ~~ r = 1.04 $.	5
1544	Find the sum of the first $ 336 $ terms of a geometric sequence if $ a_1 = 5.2 ~~ \text{and} ~~ r = 1.04 $.	5
1545	Find $ a_10 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -2 $.	5
1546	Find $ a_12 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $.	5
1547	Find $ a_7 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1548	Find $ a_10 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1549	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 60 ~~ \text{and} ~~ r = 0.6 $.	5
1550	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 61 }{ 50 } $.	5