Question

Which expression describes the nth term of the arithmetic sequence 5, 9, 13, 17, ...?

Answer 1

Answer:

4n + 1

Step-by-step explanation:

The first term is 5.

Each new term is 4 plus the previous term.

Term 1 = 5

Term 2 = 5 + 4

Term 3 = 5 + 4 + 4

Term 4 = 5 + 4 + 4 + 4

Notice that for each new term, you add one 4 less than the number of the term.

In term 1, you have 5 and no 4 added.

In term 2, you add one 4 to the 5.

In term 3, you add two 4's to the 5.

In term n, you add (n - 1) 4's to the 5.

Term n = 5 + (n - 1)4

Term n = 5 + 4n - 4

Term n = 4n + 1

Answer: 4n + 1