Question

I NEED HELP PLEASE!

Which recursive formula describes the sequence below? 5, 13, 29, 61, 125, ...
A.
`an=an-1+8;a1=5`
B.
`an=2an-1+3;a1=5`
C.
`an=3an-1-2;1a=5`
D.
`an=(an-1)^2-12;a1=5`

Answer 1

The answer is B

I just took the test i hope this helps :)

Answer 2

Option B -
`a_n=2a_(n-1)+3 ; a_1=5`

Explanation:

Given : Sequence 5, 13, 29, 61, 125, ...

To find : Which recursive formula describes the sequence below?

Solution :

To find which function gives recursive formula substitute the value and check which satisfy the given sequence.

A.
`a_n=a_(n-1)+8 ; a_1=5`

Finding 2 term put n=2

`a_2=a_(2-1)+8`

`a_2=a_(1)+8`

`a_(2)= 5+8`

`a_(2)= 13`

Applicable as second term is 13.

Check for third term put n=3

`a_3=a_(3-1)+8`

`a_3=a_(2)+8`

`a_(3)= 13+8`

`a_(3)= 21`

Not applicable as third term is 29.

B.
`a_n=2a_(n-1)+3 ; a_1=5`

Finding 2 term put n=2

`a_2=2a_(2-1)+3`

`a_2=2a_(1)+3`

`a_(2)= 2(5)+3`

`a_(2)= 13`

Applicable as second term is 13.

Check for third term put n=3

`a_3=2a_(3-1)+3`

`a_3=2a_(2)+3`

`a_(3)= 2(13)+3`

`a_(3)= 26+3`

`a_(3)= 29`

Applicable as third term is 29.

C.
`a_n=3a_(n-1)-2 ; a_1=5`

Finding 2 term put n=2

`a_2=3a_(2-1)-2`

`a_2=3a_(1)-2`

`a_(2)= 3(5)-2`

`a_(2)= 13`

Applicable as second term is 13.

Check for third term put n=3

`a_3=3a_(3-1)-2`

`a_3=3a_(2)-2`

`a_(3)= 3(13)-2`

`a_(3)= 37`

Not applicable as third term is 29.

D.
`a_n=a_(n-1)^2-12 ; a_1=5`

Finding 2 term put n=2

`a_2=a_(2-1)^2-12`

`a_2=a_(1)^2-12`

`a_(2)= 5^2-12`

`a_(2)= 13`

Applicable as second term is 13.

Check for third term put n=3

`a_3=a_(3-1)^2-12`

`a_3=a_(2)^2-12`

`a_(3)= (13)^2-12`

`a_(3)= 157`

Not applicable as third term is 29.

Therefore, Only Option B is correct as it form the recursive formula of given sequence.