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

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.

A_n= a₁+(n-1)d

a₁ first term

n terms

d distance between each value

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