Answer:
The correct answer option is: [tex]S_9=\frac{9}{2} (2+26)[/tex]
Step-by-step explanation:
We know that,
the sum of the first [tex]n[/tex] terms of an Arithmetic Sequence is given by:
[tex]S_9=\frac{n(a_1+a_n)}{2}[/tex]
where [tex]n[/tex] is the number of terms,
[tex]a_1[/tex] is the first term of the sequence; and
[tex]a_n[/tex] is the first term of the sequence.
So for [tex]a_n=3n-1[/tex],
[tex]a_1=3(1)-1=2[/tex]
and
[tex]a_9=3(9)-1=26[/tex]
Putting these values in the formula to get:
[tex]S_9=\frac{9(a_1+a_9)}{2}[/tex]
[tex]S_9=\frac{9(2+26)}{2} \\\\S_9=\frac{9}{2} (2+26)[/tex]
First five terms:
[tex]a_1=3(1)-1=2[/tex]
[tex]S_1=\frac{1(2+2)}{2}[/tex]=2
[tex]a_2=3(2)-1=5[/tex]
[tex]S_2=\frac{2(2+5)}{2}[/tex]=7
[tex]a_3=3(3)-1=8[/tex]
[tex]S_2=\frac{3(2+8)}{2}[/tex]=15
[tex]a_4=3(4)-1=11[/tex]
[tex]S_4=\frac{4(2+11)}{2}[/tex]=26
[tex]a_5=3(5)-1=14[/tex]
[tex]S_5=\frac{5(2+14)}{2}[/tex]=40
