The common difference, d in an arithmetic sequence whose fourth term is 16 and whose seventh therm is 31

Answer: d=5

Step-by-step explanation:

Arithmetic progression

An=a1+d (n-1)

An = nth term

A1 = first term

D = common difference

N = nth position

We are given the 4th and 7th terms

For 4th term, n=4

A4=a1+d (4-1)

A4 = 16

16 = a1+d (4-1)

16 = a1+3d ... equation 1

For the 7th term, n=7

A7=a1+d (7-1)

A7 = 31

31=a1+6d ... equation 2

Bring them together

16=a1+3d

31=a1+6d

Subtract equation 1 from 2

So we have

15=3d

D=15/3

D=5

Therefore, the common difference is 5