Question

In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 45/2. The sum of the two middle numbers can be written as ab where a and b are coprime positive integers. Find a+b.

Answer 1

hmm
\[12, 12r^2,12r^2\]
\[12r,12r+k,12r+2k=452\]
\[12r+k=12r^2\\ 12r+2k=452\] that would be my guess, but it is late

Answer 2

OR, 12,a,b,452