Question

An arithmetic sequence has this recursive formula: What is the explicit formula for this sequence? A. an=-6+(n-2)8 B. an=8+(n-6)(-1) C. an=8+(n-1)(-6) D. an=8+(n-1)6

Answer 1

C

Explanation:

`a_(n)-a_(n-1)=-6\\d=-6\\a_(n)=a_(1)+(n-1)d\\a_(n)=8+(n-1)(-6)`

Answer 2

an = 8 + (n-1) *(-6)

Explanation:

The explicit formula is

an = a1+ d (n-1) where a1 is the initial value and d is the common difference

The initial value is 8 so a1 = 8

The common difference is what we are adding or subtracting each time

We are subtracting 6 each time as we see from the recursive forumla

so d = -6

an = 8 -6(n-1)

or

an = 8 + (n-1) *(-6)