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;
[tex]h(2) = h(1)-10 = -75-10 = -85[/tex]
Similarly for n = 3
[tex]h(3) = h(3)-10 = -85-10 = -95[/tex] and so on...
The series we get;
[tex]-75, -85, -95, ....[/tex]
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:
[tex]a_n = a+(n-1)d[/tex]
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);
[tex]h(n) = a+(n-1)d[/tex]
Substitute the given values we have;
[tex]h(n) = -75+(n-1)(-10)[/tex]
or
[tex]h(n) = -75-10n+10 = -65-10n[/tex]
Therefore, the explicit formula for h(n) is, -65-10n
