Question

what is the nth term of the sequence 2, 5, 8, 11?

Answer 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding 33 to the previous term in the sequence gives the next term. In other words, an=a1+d(n−1)an=a1+d(n-1).
Arithmetic Sequence: d=3d=3
This is the formula of an arithmetic sequence.
an=a1+d(n−1)an=a1+d(n-1)
Substitute in the values of a1=2a1=2 and d=3d=3.
an=2+(3)(n−1)an=2+(3)(n-1)
Simplify each term.

an=2+(3n−3)an=2+(3n-3)
Simplify the expression.

an=3n−1