## Question

###### How do you find the sum of the first 16 terms of #-90+30+(-10)+10/3+...#?

How do you find the sum of the first 16 terms of #-90+30+(-10)+10/3+...#?

## Answers

Approximately

#67.5# ## Explanation:

The general equation for the sum of the first

#n# terms of a geometric series with initial value#a_1# and a common ratio of#r# is:

#color(white)("XXX")sum_(i=1)^n a_i=a_1((1-r^n)/(1-r))# In this case, the sum of the first

#15# terms with an initial value of#90# and a common ratio of#(-1/3)# is

#color(white)("XXX")90 * ((1-(-1/3)^15)/(1-(-1/3)))#

#color(white)("XXX")~~67.5000047# (assuming I used my calculator correctly)

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