Posts Tagged ‘geometric sequence’

Problem 643

Find the sixth term of a geometric sequence with t5 = 24 and t8 = 3.

 

Solution:-

 

t5 = 24 =  a*r^{4}

t8 = 3 =  a*r^{7}

Dividing one by the other

r^{3} =\frac{ 1}{8}

r = \frac{1}{2}

t6 = a*r^{5} = t5*r = 24 *\frac{ 1}{2} = 12.

So the value of sixth term 12

Problem 642

What are the next four terms in the following geometric sequence?
5, 15, 45,…

 

Solution:-

 

First we are find common ratio \frac{15}{5} = 3

In geometric sequence we have to find the next number by multiply last number to common ratio.

45*3 = 135

135 * 3 = 405

405*3 = 1215

1215*3 = 3645

So the next four terms are 135, 405, 1215, 3645

 

Problem 641

What is the common ratio of the following geometric sequence?

5, 15, 45,…

 

Solution:-

 

Common ratio = \frac{second -term}{first-term}

common ratio = \frac{15}{5}

common ratio = 3