If the second term of a geometric sequence of real numbers is -2 and the fifth term is 16 then what is the fourteenth term?
We have that
-2 = a1*(r)^(2-1) → -2 = a1*(r) (1)
And
16 = a1* (r)^(5 -1) → 16 = a1*(r)^(4) (2)
Rearrange (1) as -2/r = a1 sub this into (2)
16 = (-2/r) * (r)^4 simplify
16 = (-2) *(r)^3 divide both sides by -2
-8 = (r)^3 take the cube root of each side and -2 = r
Using -2/r = a1 → -2/-2 = a1 = 1
So....the foruteenth term is
1(-2)^(14 - 1) = 1(-2)^13 = - 8192