Identify the explicit function for the sequence in the table

X Y

1 7

2 19

3 31

4 43

5 55

Choices:

A. a (n) = 7 (n-1)

B. a (n) = 7 + (n-1) •12

C. a (n) = 12 + (n-1) •7

D. a (n) = 12 (n-1)

The common difference is 19-7 = 31-19 = 12, so this is an arithmetic sequence. The initial term (when n=1) is 7.

The explicit formula for the terms of an arithmetic sequence is

an = a1 + d (n-1)

where "a1" is the first term and "d" is the common difference. The formula that matches a1=7 and d=12 is

B. a (n) = 7 + (n-1) ·12