Question

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

Answer 1

Answer:

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