Three terms of an arithmetic sequence are shown below. which recursive formula defines the sequence? f(1) = 6, f(4) = 12, f(7) = 18

The recursive formula defines the sequence is .

Step-by-step explanation:

Three terms of an arithmetic sequence are

f(1) = 6

f(4) = 12

f(7) = 18

It means first term is 6, fourth term is 12 and seventh term is 18.

The formula for nth term of an arithmetic sequence is

where n is number of term, a is first term and d is common difference.

4th term of the AP is

Subtract 6 from both sides.

Divide both sides by 3.

The common difference is 2.

The recursive formula for an AP is

Substitute d=2 in the above equation.

It can be written as

Therefore the recursive formula defines the sequence is .