Question

Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain. n an 1 40 2 47 3 54 an = 40 + 7(n − 1) where n ≥ 40 an = 40 + 7(n − 1) where n ≥ 1 an = 40 − 7(n − 1) where n ≥ 40 an = 40 − 7(n − 1) where n ≥ 1

Answer 1

Arithmetic sequence is given 40, 47 , 54 , ........
Here you can see common difference is 7 and first term is 40 .
∴ nth term , an = a + (n - 1)d , here a is the first term and d is the common difference of given Arithmetic progression.
So, an = 40 + 7(n - 1)

Hence, answer is an = 40 + 7(n -1) , where n ≥ 1