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.
