SOLUTION: The three numbers n-2, n, n+3, are consecutive terms of a geometric progression. i) Find n and the term after n+3

From the condition, you have this equation


    (n-2)*(n+3) = n^2.


Simplify


    n^2 + n - 6 = n^2

          n     = 6.     


So, n = 6;  the first three terms are  4, 6, 9,  and the next term is   =  =  =   = 13.5.     ANSWER