Question

A certain arithmetic sequence has the following explicit formula for the nth term: an = 4 + (n - 1)(7) The same sequence has the following recursive formula: an = an-1 + _____ What number belongs in the blank space in the recursive formula?

Answer 1

an = 4 + (n - 1)(7) 

a1 = 4 + (1-1)*7 = 4
a2 = 4 + (2-1)*7 = 4 + 7

$a_{n} = a_{n-1} +7$

7 is common difference of arithmetic sequence.

Answer 2

Answer: $a_n=a_{n-1}+7$

Step-by-step explanation:

We know that the nth term in Arithmetic sequence is given by :-

$a_n=a+(n-1)d$..................(1)

Given: A certain arithmetic sequence has the following explicit formula for the nth term:

$a_n=4+(n-1)(7)$.............................(2)

When we compare (1) and (2), we get

$d=7$

Also, the recursive formula in A.P. can be written as

$a_n=a_{n-1}+d$

Therefore, The same sequence has the following recursive formula:

$a_n=a_{n-1}+7$