Respuesta :
Answer:
Option A is correct.
The equation = [tex]S_9 =\frac{9}{2} (2+26)[/tex].
Explanation:
Sum of the terms of an arithmetic series is given by
[tex]S_n = \frac{n(a_1+a_n)}{2}[/tex], ......[1]
where n is the number of terms, [tex]a_1[/tex] is the first term and [tex]a_n[/tex]is the last term.
Given the formula for nth term in the arithmetic sequence is, [tex]a_n = 3n-1[/tex]
for n =1
[tex]a_1 = 3 \cdot 1 -1 = 3-1 =2[/tex]
for n =9
[tex]a_9= 3 \cdot 9 -1 = 27-1 =26[/tex]
Then, put these values in equation [1] for n =9;
[tex]S_9 = \frac{9 \cdot (a_1+a_9)}{2} = \frac{9(2+26)}{2}[/tex] or
[tex]S_9 =\frac{9}{2} (2+26)[/tex]
Therefore, the equation is; [tex]S_9 =\frac{9}{2} (2+26)[/tex]
