Given:
[tex]h(n)=-91\cdot\left(-\dfrac{1}{7}\right)^{\large{\,n-1}}[/tex]
To find:
The recursive formula.
Solution:
We have,
[tex]h(n)=-91\cdot\left(-\dfrac{1}{7}\right)^{\large{\,n-1}}[/tex]
It is in the form of explicate formula of a GP, .i.e., [tex]a_n=ar^{n-1}[/tex].
Here, [tex]a=-91[/tex] and [tex]r=-\dfrac{1}{7}[/tex].
The recursive formula of a GP is
[tex]a_n=a_{n-1}\times r[/tex]
Using this the recursive formula for given problem is
[tex]h(n)=h(n-1)\times (-\dfrac{1}{7})[/tex]
Therefore, the required recursive formula is [tex]h(n)=h(n-1)\times (-\dfrac{1}{7})[/tex].
