ANSWER
[tex]S_5= 42.5[/tex]
EXPLANATION
The general term of the arithmetic sequence is
[tex]a_n=1+\frac{5}{2}n[/tex]
For the first term,we substitute [tex]n=1[/tex] to get,
[tex]a_1=1+\frac{5}{2}\times 1[/tex]
[tex]a_1=1+2.5=3.5[/tex]
Similarly
[tex]a_5=1+\frac{5}{2}\times 5[/tex]
[tex]a_5=13.5[/tex]
The sum of the first n-terms is given by the formula,
[tex]S_n=\frac{n}{2}(a_1+l)[/tex]
where l is the last term.
In this case
[tex]l=a_5=13.5[/tex]
We substitute these values to get,
[tex]S_5= \frac{5}{2} (3.5 + 13.5)[/tex]
[tex]S_5= \frac{5}{2} (17)[/tex]
[tex]S_5=42.5[/tex]
We could have also used the formula,
[tex]S_n=\frac{n}{2}(2a_1+(n-1)d)[/tex]
[tex]S_5=\frac{5}{2}(2(3.5)+(5-1)2.5)[/tex]
[tex]S_5=42.5[/tex]
