Which Represent the first two terms of the sequence a1=2 and an=-2(an-1)^2
2, -8
-8,-128
16,1024
-2,16
You already know that the first term is a1 = 2
The second term is given by the reucrsion formula
a2 = (-2)*(a1)^2 = -2 * 4 = -8
To find the first two terms of the sequence defined by a1 = 2 and an = -2(an-1)^2, we can use the given formula and substitute the values accordingly.
First Term (a1):
Using the given formula, substitute n = 1:
a1 = -2(a1-1)^2
a1 = -2(2-1)^2
a1 = -2(1)^2
a1 = -2(1)
a1 = -2
Second Term (a2):
Using the given formula, substitute n = 2 and the previous term a1 = -2:
a2 = -2(a2-1)^2
a2 = -2(-2-1)^2
a2 = -2(-3)^2
a2 = -2(9)
a2 = -18
Therefore, the first two terms of the sequence are:
a1 = -2
a2 = -18
Neither of the answer choices provided (2, -8; -8, -128; 16, 1024; -2, 16) matches the correct first two terms of the sequence.