Question

Find a formula for the nth term in this

arithmetic sequence:
a1 = 9, a2 = 13, a3 = 17, a4 = 21, ...
an =?n+

Answer 1

Answer: an=4n+5

Explanation:

a1 = 9, a2 = 13, a3 = 17, a4 = 21, ...

A formula for the nth term of the arithmetic sequence:

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

where: a₁ - is the first term of the arithmetic sequence

d - is the difference between the terms of the arithmetic sequence

d=a₂-a₁=a₃-a₂=a₄-a₃= ...

d=13-9=17-13=31-17= ...

d=4

n - is the number of the arithmetic sequence term

`a_n=9+4(n-1)\\\\a_n=9+4n-4\\\\a_n=4n+5`