Question

An arithmetic sequence has this recursive formula

Answer 1

Answer: B
This is because 7 is standing in place for a1 and -4 is standing in place for d in the explicit equation: an=a1+(n-1)d

Answer 2

`\text{The explicit formula is }a_n=7+(n-1)(-4)`

Option B is correct.

Explanation:

Given the recursive formula of arithmetic sequence

`a_1=7`

`a_(n)=a_(n-1)-4`

we have to find the explicit formula for the above sequence.

`a_(n)=a_(n-1)-4`

`a_(n)-a_(n-1)=-4`

which is the common difference, d=-4

The explicit formula for A.P is

`a_n=a_1+(n-1)d`

`a_n=7+(n-1)(-4)`

Option B is correct.