This is definitely a case of geometric progressions.
The first value (first payment) is $150. Â The next is $150*1.3; the next is $150*1.3*1.3. Â And so on. Â The formula used to determine the nth payment isÂ
Pn = P*r^(n-1), where P is the first payment and n is the index. Â For the first payment, n=1 and the predicted payment is $150*1.3^(1-1) = $150, as expected.
Â
We want to find the sum of this person's first 15 payments. Â The formula for the sum of the first n payments is
      Â
      1-r^n
Sn = ---------- , and r = 1.3 in this case and n=15.
       1-r
             1 - 1.3^15
Thus, S_15 = -----------------
               1-1.3