The nth term of an arithmetic sequence is given. an = 6 + 3(n − 1)

Question

The nth term of an arithmetic sequence is given.

a_n = 6 + 3(n − 1)

(a) Find the first five terms of the sequence.

a1	=
a2	=
a3	=
a4	=
a5	=

(b) What is the common difference d?

d = 

Answer 1

an= 6 +3(n-1) = 6+3n-3= 3+3n

a1 = 3+3= 6

a2 = 3+6 =9

a3 = 3+9 =12

a4 = 3+12 =15

a5 = 3+15 = 18

common difference = d = 3

Answer 2

To find the first term (also known as a₁), then plug in n = 1 into the equation 6 + 3(n − 1)

To find the 2nd term (also known as a₂), then plug in n = 2 into the equation 6 + 3(n − 1)

To find the 3rd term (also known as a₃), then plug in n = 3 into the equation 6 + 3(n − 1)

To find the 4th term (also known as a₄), then plug in n = 4 into the equation 6 + 3(n − 1)

To find the 5th term (also known as a₅), then plug in n = 5 into the equation 6 + 3(n − 1)

The common difference is the number that separates each term.