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

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