Question

three numbers are in harmonic progression. If the third number were decreased by 4 they would
be in arithmetic progression. If the third number were decreased by 3 they would be in geometric
progression. Find the third term of the harmonic progression.

Answer 1

1/b - 1/a = 1/c - 1/b
b-a = (c-4)-b
b/a = (c-3)/b

I get c=12

Answer 2

how do i first derive the equation?