Question

Find a formula for the nth term in thisarithmetic sequence:a1= 9, a2 = 13, a3 = 17, a4 = 21,a, = 0?]n + [

Answer 1

Since the first 4 terms of the sequence are

9, 13, 17, 21

Since the difference between each 2 conescutive terms is

13 - 9 = 4

17 - 13 = 4

21 - 17 = 4

Then the constant difference is 4

Since the rule of the nth term is

`a_n=a_1+(n-1)d`

Since the first term is 9, then

a1 = 9

Since d is the constant difference, then

d = 4

Substitute them in the rule above

`\begin{gathered} a_n=9+(n-1)4 \\ a_n=9+4n-4 \end{gathered}`

Add the like terms

`a_n=5+4n`

The answer is

`a_n=5+4n`