Question

An arithmetic sequence has a third term of 7 and a fifth term of 13. Write an equation could be used to find the both term of the sequence.

Answer 1

a(n) = 3n - 2.

Explanation:

The nth term of an arithmetic sequence = a1 + d(n - 1) where a1 = the first term and d = the common difference.

So here we have:

a3 = 7 = a1 + 2d

a5 = 13 = a1 + 4d

Rewriting:

a1 + 4d = 13

a1 + 2d = 7

Subtracting, we eliminate a1:

2d = 6

d = 3

and a1 = 7 - 2(3)

= 1.

So our equation we can use to find any term is

a(n) = 1 + 3(n - 1)

a(n) = 1 + 3n - 3

a(n) = 3n - 2 (answer).

Checking :

3rs term = 3(3) - 2 = 7.

5th term = 3(5) - 2 = 13.

First term = 3(1) - 2 = 1.