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

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.

addition

step-by-step explanation: