Answer:
[tex]193.5[/tex]
Step-by-step explanation:
The first term of this sequence is a=1.
The last term of the sequence is
[tex]9 \frac{3}{4} [/tex]
The common difference is d=1.25-1=0.25
We can determine the number of terms in the sequence using
[tex]a_n=a+d(n-1)[/tex]
That is:
[tex]9.75=1+0.25(n-1)[/tex]
[tex]9.75=1+0.25n-0.25[/tex]
[tex]9.75 - 1 + 0.25=0.25n[/tex]
[tex]9 = 0.25n[/tex]
[tex]n = \frac{9}{0.25} = 36[/tex]
The sum of the terms is given by
[tex]S_n = \frac{n}{2} (a + l)[/tex]
This implies that:
[tex]S_{36}= \frac{36}{2} (1 + 9.75)[/tex]
[tex]S_{36}=18(10.75)[/tex]
[tex]S_{36}=193.5[/tex]
