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)

The correct answer is b.)

Step-by-step 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!