Question

What is the explicit formula represented by this graph?

A) an = −1 − 1 (n−1)
B) an = 1 + 1 (n−1)
C) an = 3 + 2 (n−1)
D) an = 3 − 2 (n−1)

Answer 1

Answer: aₙ = 3 + 2(n - 1)

Explanation:

The points fall on a straight line, so we have an arithmetic sequence.

The explicit formula for an arithmetic sequence is

aₙ = a₁ + d(n -1 )

Data:

a₁ = 3

a₂ = 5

Answer 2

aₙ = 3 + 2(n - 1)

Explanation:

The points fall on a straight line, so we have an arithmetic sequence.

The explicit formula for an arithmetic sequence is

aₙ = a₁ + d(n -1 )

Data:

a₁ = 3

a₂ = 5

Calculations:

d is the difference in value between two consecutive terms.

For example,

d = a₂ - a₁ = 5 - 3 = 2

Insert the value of d

aₙ = a₁ + 2(n -1 )

Insert the value of a₁

aₙ = 3 + 2(n - 1)

Note: This sequence starts with n = 0, but the formula still works.