Question

Which recursive formula can be used to generate the sequence shown, where f(1) = 5 and n > 1? 5,–1, –7, –13, –19, ...

Answer 1

a+(n-1)d is te formula

Answer 2

Answer:

The recursive formula of given sequence is $f(n)=f(n-1)-6$,where f(1) = 5 and n > 1.

Step-by-step explanation:

The given sequence is

5,–1, –7, –13, –19, ...

Here first term is 5 and the common difference is

$d=a_2-a_1=-1-5=-6$

The nth term of an AP is

$a_n=a+(n-1)d$

We know that in an AP,

$a_n-a_{n-1}=d$

$a_n=a_{n-1}+d$

For given sequence

$a_n=a_{n-1}-6$

It can be written as

$f(n)=f(n-1)-6$

Therefore the recursive formula of given sequence is $f(n)=f(n-1)-6$,where f(1) = 5 and n > 1.