Question

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

Answer 1

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