Question

What is the explicit formula for this sequence?

-7, -4, -1, 2, 5...

a.) an = 8 + (b - 1)3
b.) an = -7 + (n - 1)3
c.) an = 3 + (n -1) (-7)
d.) an = -7 + (n - 1)(-3)

Answer 1

The correct answer is b.)

Explanation:

Given:

Sequence -7, -4, -1, 2, 5....... => a₁ = -7, a₂ = -4, a₃ = -1, a₄ = 2 and a₅ = 5

We conclude that this sequence is arithmetic series.

First we must find difference d:

d = a₂ - a₁ = a₃ - a₂ = -4 - (-7) = -1 - (-4) = -4 + 7 = -1 + 4 = 3

d = 3

The formula for n-th term of the arithmetic series is:

aₙ = a₁ + (n-1) d

aₙ = -7 + (n-1) 3

God with you!!!