Question

Help me pls Represent the arithmetic series using the recursive formula.

Answer 1

Answer:

Option C) is correct

That is the given arithmetic sequence represents the recursive formula is f(n)=f(n-1)+(-5)

Step-by-step explanation:

The given arithmetic sequence is ${\{94,89,84,79,...}\}$

Let f(1)=94,f(2)=89,f(3)=84,...

To find the common difference d :

$d=f(2)-f(1)$  ,

$=89-94$

$=-5$

Therefore d=-5

$d=f(3)-f(2)$  ,

$=84-89$

$=-5$

Therefore d=-5

Therefore the common difference d=-5

check the recursive formula  $f(n)=f(n-1)+d$ which represents the given arithmetic sequence

Put n=2  and d=-5 in $f(n)=f(n-1)+d$ we get

$f(2)=f(2-1)+(-5)$

$=f(1)-5$

$=94-5$

Therefore f(2)=89

Put n=3  and d=-5 in $f(n)=f(n-1)+d$ we get

$f(3)=f(3-1)+(-5)$

$=f(2)-5$

$=89-5$

Therefore f(3)=84

and so on

Therefore the recursive formula $f(n)=f(n-1)+d$ where d=-5

Therefore the recursive formula $f(n)=f(n-1)+(-5)$  represents the given arithmetic sequence