Hello from MrBillDoesMath!
Answer:
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