Question

Find the sum of a finite geometric series.

The Smiths spent $2,000 on clothes in a particular year. If they increase the amount they spend on clothes by 10% each year, the Smiths will spend a total of $
on clothing in 4 years.

Answer 1

sum of a finite geometric series=a(r^(n) -1)/(r -1)
or
sum of a finite geometric series=a(1 - r^(n))/(1 - r)
the Smiths would spend a total of $2928.2 on clothing in 4 years

Answer 2

Including the first year where they spend $2,000 dollars and it's added altogether: $9,282

Not including first year and it's added altogether: $10,210.2

If you're talking about the money they spent on only the 4th year:
1st year- $2,000
2nd year- $2,200
3rd year- $2,420
4th year- $2,662

If you don't count the year where they spend $2,000:
1st year: $2,200
2nd year: $2,420
3rd year: $2,662
4th year: $2,928.2