Unit K: Student Problem 10

We split up the decimal and know that the first term would be .4. That becomes 4 over 10 (we want to use fractions in this problem). To Find r, we put the second term over the first term, so: .04 over .4 which equals .1.

Next we need to plug into our infinite geometric formula.  The first term is 4/10, so we write that, and multiply by .1 (which is r) raised to n-1. We multiply this out and cross cross the denominator with the reciprocal, we are left with 4/9.

This problem is about using the infinite geometric formula for a sequence with a repeating decimal (we need to rationalize it). You should pay attention to cross canceling and plugging things in to the correct area.