Question

The first term of a geometric series is a/b^2, and the common ratio is b/a^2. Find the next five terms of the geometric sequence.

Answer 1

Here it is in order (2nd to 6th):
1/ab, 1/a^3, b/a^5, b^2/a^7, b^3/a^9

Hope this helps!

Answer 2

Answer:

the next five terms are:

$\frac{1}{ab} , \frac{1}{a^{3} } ,\frac{b}{a^{5} } ,\frac{b^{2} }{a^{7} } ,\frac{b^{3} }{a^{9} }$

Step-by-step explanation:

A geometric serie is a succession of terms on which every terms is the result of the last term multiply to a common ratio. for example, a geometric serie with inicial terms equal to 2 and the common ratio is 3, the four first numbers of the serie is given by

2, 6, 18, 54

Where every term is calculate as:

first term = 2

second term = first term x common ratio = 2 * 3 = 6

third term = second term x common ratio = 6 * 3 = 18

fourth term = third term x common ratio= 8 * 3 = 54

Then, with this exercise we have the same situation, the first term is $\frac{a}{b^{2} }$ and the common ratio is $\frac{b}{a^{2} }$, so we get:

first term = $\frac{a}{b^{2} }$

second term = first term * common ratio = $\frac{a}{b^{2} } *\frac{b}{a^{2} } = \frac{1}{ab}$

third term = second term * common ratio = $\frac{1}{ab} *\frac{b}{a^{2} } =\frac{1}{a^{3} }$

fourth term = third term * common ratio = $\frac{1}{a^{3} } *\frac{b}{a^{2} } = \frac{b}{a^{5} }$

fifth term = fourth term * common ratio= $\frac{b}{a^{5} } *\frac{b}{a^{2} } = \frac{b^{2} }{a^{7} }$

sixth term = fifth term * common ratio= $\frac{b^{2} }{a^{7} } *\frac{b}{a^{2} } = \frac{b^{3} }{a^{9} }$

so, the next five terms are:

$\frac{1}{ab} , \frac{1}{a^{3} } ,\frac{b}{a^{5} } ,\frac{b^{2} }{a^{7} } ,\frac{b^{3} }{a^{9} }$