Find the eighth term of the geometric sequence whose second and fourth terms are -8 and -32. A)a₈ = -3,072 B)a₈ = -512 C)a₈ = -1,024 D)a₈ = -256 E)a₈ = -128

Question

Quizplus · Accepted Answer

Let the first term be a and the common ratio be r.
According to the problem,
ar = -8 (1)
ar^3 = -32 (2)
Dividing (2) by (1), we get:
r^2 = 4
r = ±2 (we discard the negative value as it doesn't make sense in the context of the problem)
Substituting r = 2 in (1), we get:
a = -4
So, the sequence is: -4, -8, -16, -32, ...
The eighth term can be found using the formula:
an = a * r^(n-1)
Substituting n = 8, a = -4, and r = 2, we get:
a8 = -4 * 2^(8-1) = -512
Therefore, the eighth term is -512.

Find the Eighth Term of the Geometric Sequence Whose Second