Question

The first term of an arithmetic sequence is 4 and the fifth term is 16. What is the nth term of the sequence?

Answer 1

First term, a = 4

Fifth term = 16

The nth term of arithmetic sequence :  a + (n - 1)*d

For fifth term, n = 5

a + (n - 1)*d

Substitute n = 5, a = 4, d = ?, 5th term = 16

4 + (5 - 1)d = 16

4 + 4d = 16

4d = 16 - 4

4d = 12    Divide by 4

d = 12/4

d = 3.

Recall the nth term is:     a + (n - 1)*d = 4 + (n - 1)*3

4 + (n - 1)*3

4 + 3n - 3

3n + 4 - 3

3n + 1

So the nth term is 3n + 1.   Option B.

Hope this helps