Question

A select choice are. definition A or. definition BB select choice are. table A. or. table B

Answer 1

Given:

The sequence is :

`2,5,\ldots`

Now,

(a)The recursive formula for the given sequence is given by:

Definition 1:

`a(n)=a(n-1)+3`

If we put n =2 , we have:

`\begin{gathered} a(2)=a(1)+3 \\ a(2)=2+3 \\ a(2)=5 \end{gathered}`

Hence, it satisfies the given sequence since it returns the numbers: 2 , 5 , ...

Definition(2):

`\begin{gathered} a(n)=a(n-1)-3 \\ a(2)=a(1)-3 \\ a(2)=2-3 \\ a(2)=-1 \end{gathered}`

But the second element is 5 so it does not satisfy the recursive relation.

Definition A is correct

(b)

The table that returns correct values of recursive relation is:

From the recursive relation given in definition (1):

The elements are given as:

For n = 1 a(n) = 2

For n = 2 a(n) = 5

For n= 3 a(n)= a(3-1) +3 = a(2)+ 3 = 5 + 3 = 8

For n= 4 a(n) = a(4 - 1 ) +3 = a(3) + 3 = 8 + 3 = 11

Hence,

Table B matches the correct values of the recursive relation.

Hence, table B is correct.