Question

A certain arithmetic sequence has this explicit formula for the nth term: an = 11 + (n – 1)(4) The same sequence has this recursive formula: an = an–1 + What number belongs in the blank space in the recursive formula?

a.15
b.11
c.3
d.4

Answer 1

I would say D

Answer 2

4

Explanation:

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

`a_n = 11 + (n- 1)(4)`

Substitute n = 1

`a_1 = 11 + (1- 1)(4)`

`a_1 = 11`

Substitute n =2

`a_2 = 11 + (2- 1)(4)`

`a_2 = 15`

`d= a_2-a_1=15-11=4`

So,
`a_2=a_1+d=11+4=15` --1

Substitute n = 3

`a_3 = 11 + (3- 1)(4)`

`a_3 = 19`

`a_3=a_2+d=15+4=19` ---2

So, with 1 and 2

Recursive formula :
`a_n=a_(n-1)+d`

Since d is 4

So, the number belongs in the blank space in the recursive formula is 4.