the first term of an arithmetic sequence is 4 and the fifth term is 16 what is the 9th number in the sequence

The 9th number is 28.

Step-by-step explanation:

Represent the common difference by d and the first term by f.

We can then write a formula for the nth term of this arithmetic sequence as follows;

a (n) = f+d (n-1)

We are told that the fifth term is 16; therefore, a (5) = 4+d (5-1) = 16. We need to solve this equation for d.

Performing the indicated multiplication: 4 + 4d = 16.

Subtracting 4 from both sides: 4d = 12

Isolating d by dividing both sides by 4: d = 3

Then the general formula for this sequence is a (n) = 4 + 3 (n-1).

The 9th number in this sequence is thus a (9) = 4 + 3 (9-1), or

a (9) = 4 + 3 (8) = 28