Find a function that describes the sequence. use y for the term in the sequence and n for its place in the list. then use the function to find the next three terms in the sequence. 7.5, 8.5, 9.5, 10.5, . . a. y = n + 6.5; 11.5, 12.5, 13.5 c. y = 6.5n +1; 33.5, 40, 46.5 b. y = 7.5n; 37.5, 45, 52.5 d. y = 8.5n –1; 41.5, 50, 58.5

This is an arithmetic sequence because each term is a constant difference, called the common difference, with respect to the previous term.  Any arithmetic sequence can be expressed as:

a(n)=a+d(n-1), a(n)=nth term, a=initial term, d=common difference, n=term number

d=8.5-7.5=9.5-8.5=10.5-9.5=1, and a=7.5 so

a(n)=7.5+1(n-1)

a(n)=7.5+n-1

a(n)=n+6.5, or using the variable label asked for in the question:

y=n+6.5

And the next three terms when n=5,6, and 7 will be 11.5, 12.5, and 13.5

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