Question

Please help, thank you!

Match the sequence and recursive expression to its explicit expression. f(n) = 2n + 10

{2, 4, 6, 8...} ...} f(1) = 2 and f(n) = f(n - 1) + 2 for n >


{12, 14, 16, 18...} f(1) = 12 and f(n) = f(n - 1) + 2 for n > 1

Answer 1

Given:

`f(n)=2n+10`

To find:

The sequence and recursive expression to the given explicit expression.

Solution:

We have,

`f(n)=2n+10`

For n=1,

`f(1)=2(1)+10`

`f(1)=2+10`

`f(1)=12`

The value of f(1) is 12.

Similarly,

For n=2,

`f(2)=2(2)+10=14`

For n=3,

`f(3)=2(3)+10=16`

For n=4,

`f(2)=2(4)+10=18`

The required sequence is {12,14,16,18,...}.

The recursive expression of an AP is

`f(n)=f(n-1)+d`

where, d is common difference.

Here d=2,

`f(n)=f(n-1)+2`

Therefore, the recursive expression is
`f(n)=f(n-1)+2`.