Suppose that a, b, and c are three consecutive terms in a geometric sequence. Show that 1/a+b, 1/2b, and 1/c+b are three consecutive terms in an arithmetic sequence.
so far i have:
c / b = b / a
since they are consecutive terms in a geometric sequence.
then i cross multiplied so i have ac = b^2
i don't know what to do after this. please help or give me a hint if you know how to do this problem.