Question

In an arithmetic sequence, the first term, a1, is equal to 5 and the 3rd term, a3, is equal to 9.Which number represents the common difference of the arithmetic sequence?

Answer 1

common difference d = 2

Explanation:

the nth term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

a₁ is the first term, d the common difference, n the term number

given a₃ = 9 , then

a₁ + 2d = 9 ← substitute a₁ = 5

5 + 2d = 9 ( subtract 5 from both sides )

5 - 5 + 2d = 9 - 5 ( simplify both sides )

2d = 4 ( divide both sides by 2 )

`(2)/(2)` d =
`(4)/(2)` , that is

d = 2

the common difference d = 2