Question

Find the sum of the first 45 terms in this geometric series -.5+1.5-4.5,...

Answer 1

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