Question

Select the sequence that matches the recursive formula. a1 = 39 1n = an-1 -5.

...m-9,-27,-81... ...

,34,29,24... ...,

-27,84,-243... ...,

-8.3,-7.4,-6.5...

Answer 1

From what you wrote I can assume thad difference of sequence is equal to -5.
The only matching sequence for that recursive formula is the second one:
..., 34, 29, 24, ...

Answer 2

Option 2nd is correct

39, 34, 29, 24,....

Explanation:

Given the recursive formula:

`a_1 = 39`

`a_n = a_(n-1)-5`

For n = 2

`a_2 = a_(2-1)-5`

⇒
`a_2 = a_(1)-5=39-5 = 34`

⇒
`a_2 = 34`

For n= 3:

`a_3 = a_(3-1)-5`

⇒
`a_3= a_(2)-5=34-5 = 29`

⇒
`a_3= 29`

For n = 4:

`a_4 = a_(4-1)-5`

⇒
`a_4= a_(3)-5=29-5 = 24`

⇒
`a_4= 24` and so on....

We get the sequence:

39, 34, 29, 24,....

Therefore, the sequence that matches the recursive formula is, 39, 34, 29, 24,....