Consider the sequence: 12, 17, 22, ..., ..., ... What is the 405th term of this sequence?

A_n = a₁ + (n-1) d

a₁ first term

n terms

d distance between each value

a_n = 12 + (405-1) (5) = 2032

The first term of the sequence is 12. You can also tell that you’re adding five after the first term.

12+5 (x-1) = y

Since you’re not automatically adding it on the first term, you need to subtract one from x.

You could also do this.

7+5x=y

You would still get the same number.

Let’s plug 405 in for x in the equations.

12+5 (405-1)

12+5 (404)

12+2020

2032

Let’s see if it’s the same thing in the second equation.

7+5 (405)

7+2025

2032

The 405th term is 2032.