Question

H(n)=-91\cdot\left(-\dfrac{1}{7}\right)^{\large{\,n-1}}h(n)=−91⋅(− 7 1 ​ ) n−1 h, left parenthesis, n, right parenthesis, equals, minus, 91, dot, left parenthesis, minus, start fraction, 1, divided by, 7, end fraction, right parenthesis, start superscript, n, minus, 1, end superscript Complete the recursive formula of h(n)h(n)h, left parenthesis, n, right parenthesis.

Answer 1

Given:

`h(n)=-91\cdot\left(-(1)/(7)\right)^{\large{\,n-1}}`

To find:

The recursive formula.

Solution:

We have,

`h(n)=-91\cdot\left(-(1)/(7)\right)^{\large{\,n-1}}`

It is in the form of explicate formula of a GP, .i.e.,
`a_n=ar^(n-1)`.

Here,
`a=-91` and
`r=-(1)/(7)`.

The recursive formula of a GP is

`a_n=a_(n-1)* r`

Using this the recursive formula for given problem is

`h(n)=h(n-1)* (-(1)/(7))`

Therefore, the required recursive formula is
`h(n)=h(n-1)* (-(1)/(7))`.