Answer :

Answer:

Nmber of terms in the series = 4,

Step-by-step explanation:

0.5, -0.1, 0.02

The common ratio

= -0.1 / 0.5 = -0.2
Confirm:

-0.1 * -0.2 = 0.02.

Sum of n terms

= Sn = a * (r^n - 1) / (r - 1 )    where r = the common ratio and a = the first term)

So we have:

0.416 = 0.5 * ((-0.2)^n - 1)) / (-1.2)

0.5 ((-0.2)^n - 1))  = (0.416 * (-1.2))

((-0.2)^n - 1)) = 2(0.416 * (-1.2 ))

(-0.2)^n = 2(0.416 * (-1.2)) + 1

(-0.2)^n = 0.0016

(-0.2)^4 = 0.0016

--> n = 4.