Question

The graph of an arithmetic sequence is shown. What is the value of the fourth term?

Answer 1

Answer: the fourth term is 11.5

Step-by-step explanation:

Looking at the graph of a(n) on the y(vertical) axis and n on the x(horizontal) axis, the slope is expressed as

(y2-y1)/(x2-x1) = (4 - 10)/(5 - 1) = -6/4

Slope = -1.5

This means that in the arithmetic sequence, each successive term differs by - 1.5.

The first term of the sequence is 10. It started decreasing.

The formula for the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a is the first term

n is the number of terms

d is the common difference

From the information given,

a = 10

d = -1.5

n = 4( we want to determine the value of the term). Therefore

T4 = 10 + (4-1)× -1.5

T4 = 10 + (3×-1.5)

T4 = 10 - 4.5 = 11.5