Answer:
-24
Step-by-step explanation:
We are given that
[tex]b(n)=-8-2(n-1)[/tex]
We have to find the 9th term in the sequence.
Substitute n=1
Then, we get
[tex]b(1)=-8[/tex]
Substitute n=2
Then,we get
b(2)=-8-2(2-1)=-8-2=-10
n=3
b(3)=-8-2(3-1)=-8-4=-12
[tex]d_1=b(2)-b(1)=-10-(-8)=-2[/tex]
[tex]d_2=b(3)-b(2)=-12-(-10)=-2[/tex]
[tex]d_1=d_2=d=-2[/tex]
When the difference between two consecutive terms is constant then, the sequence is called arithmetic sequence.
Therefore, the given sequence is in A.P
The nth term of A.P is given by
[tex]a_n=a+(n-1)d[/tex]
We have, [tex]a=b(1)=-8[/tex]
[tex]d=-2[/tex]
n=9
Substitute the values in the formula
[tex]a_9=-8+(9-1)(-2)=-8-16=-24[/tex]
[tex]a_9=b(9)=-24[/tex]
