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.

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

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