Question

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)

Answer 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