Answer:
B) 399
Step-by-step explanation:
We want to find the sum of the arithmetic series given that:
[tex]a_1=9, \, d = 3, \text{ and } n = 14[/tex]
In other words, we want to find the sum of the first 14 terms of the series when the first term is 9 and the common difference is 3.
Recall that the sum of an arithmetic series is given by:
[tex]\displaystyle S = \frac{n}{2}\left(a + x_n\right)[/tex]
Where n is the amount of terms, a is the first term, and xₙ is the nth or last term.
We will need to find the last term. We can write a direct formula. The general form of a direct formula is given by:
[tex]x_n=a+d(n-1)[/tex]
Since the initial term is 9 and the common difference is 3:
[tex]x_n=9+3(n-1)[/tex]
Then the 14th or last term is:
[tex]\displaystyle x_{14}=9+3((14)-1)=9+39=48[/tex]
Then the sum of the first 14 terms is:
[tex]\displaystyle \begin{aligned} S_{14} &= \frac{14}{2}\left(9+48\right) \\ \\ &= 7(57) \\ \\ &= 399\end{aligned}[/tex]
Our answer is B.
