Question

I know that: the first term of the sequence is -2, and the fifth term is - 1/8 . What is the 2nd term, 3rd term 4th term do you know?

Answer 1

Solution

Here the first term = -2

5th term = -1/8

Now we have to find the common ratio (r)

Fifth term A5 = -1/8

-1/8 =$a_{1} r^{4}$

Here $a_{1} = -2$

Plug in $a_{1}  = -2$ in the fifth term and find the value of r.

-1/8 = -2$r^{4}$

$r^{4} = \frac{-1/8}{-2}$

$r^{4} = \frac{1}{16}$

Taking 4th root, we get

r = $\frac{1}{2}$

Now let's find the second term.

$a_{2} =$ first term *r = -2 *1/2 = -1

2nd term = -1

3rd term = second term * 1/2 = -1 * 1/2 = -1/2

4th term = 3rd term *r = -1/2 *1/2 = -1/4

Thank you :)