Find the 8th term and the recursive formula . -2,12,-72,

Hello from MrBillDoesMath!

8th term: 559,872

Recursive formula: a(n+1) =  -6 * a(n),  n >=1, a(1) = -2

Discussion:  

Term "n"  (n > 1) in the series appears to equal -6 time term (n-1). That is

a(n)  = -2* (-6)^(n-1) n >= 1

a(1) = -2 * 1 = -2

a(2) = -2(-6)^(2-1) = -2 * (-6) = 12

a(3) = -2(-6)^(3-1) = -2 * (-6)^2 = -2 * 36 = -72

a(8) = -2 (-6)^(8-1)

      = -2 * (-6)^7

      = -2 * (-279936)

      = + 559872

Recursive formula:

First, a(n) = -2(-6)^(n-1) so

                 a(n+1) = -2 ( -6) ^(n+1 -1)

                           = -2 (-6)^n                    => as -6/-6 = 1

                           = -2  (-6/-6) (-6)^n

                           = -2 * -6 * (-6)^(n-1)

                           = -6 * ( -2 * (6)^(n-1))

                           = -6 a(n)

Thank you,

MrB