Answer:
S45 = -3.6875×10^20
Step-by-step explanation:
Given the geometric series
-0.5+1.5-4.5+...
The common ratio r = +1.5/-0.5 = -4.5/1.5 = -3
Since the common ratio is less than 1
Sum of geometric series will be calculated using the formula below:
Sn = a(1-r^n)/1-r
Where n is the number of terms = 45
a is the first term of the series = -0.5
r is the common ratio = -3
Substituting this values into the formula
S45 = -0.5{1-(-3)^45}/1-(-3)
S45 = -0.5{1-(-3)^45}/4
S45 = -0.5{1-(-2.95×10²¹}/4
S45 = -0.5(1+2.95×10²¹)/4
S45 = (-0.5-1.47×10²¹)/4
S45 = -1.475×10²¹/4
S45 = -3.6875×10^20
