Question

Consider the first four terms of the sequence below.

Answer 1

Answer:

a₈ = -  1 / 128

Step-by-step explanation:

Given:

First four terms of the sequence

a₁= 1, a₂= - 1/2, a₃= 1/4 and a₄= -1/8

First we recognize that this is a geometric series (sequence) and we must calculate quotient q.

q = a₂/a₁ = a₃/a₂ = (-1/2)/1 = (1/4)/(-1/2) = - 1/2

q = - 1/2

Formula for calculating n-th term is:

aₙ = a₁ · qⁿ⁻¹

According to this:

a₈ = 1  (-1/2)⁷ = - 1/ 128

God with you!!!