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

Answer:

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

Option B is correct.    

Step-by-step 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.