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 $f(n)=f(n-1)+2$.