Question

⎩

Answer 1

Answer:

h(n)=0-9(n-1)

Step-by-step explanation:

Answer 2

Answer:

the explicit formula for h(n) is, -65-10n

Step-by-step explanation:

Given that:

h(1) = -75

h(n) = h(n-1)-10              ......[1]

Put n =2 in [1] we have;

$h(2) = h(1)-10 = -75-10 = -85$

Similarly for n = 3

$h(3) = h(3)-10 = -85-10 = -95$ and so on...

The series we get;

$-75, -85, -95, ....$

This is an arithmetic sequence series with common difference(d) = -10

Since,

-85-(-75) = -85+75 = -10,

-95-(-85) = -95+85 = -10 and so on

First term(a) = -75

the Explicit formula for arithmetic sequence is given by:

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

where a is the first term,

d is the common difference and

n is the number of terms.

We have to find the explicit formula for h(n);

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

Substitute the given values we have;

$h(n) = -75+(n-1)(-10)$

or

$h(n) = -75-10n+10 = -65-10n$

Therefore, the explicit formula for h(n) is, -65-10n