Question

Find the sum of the arithmetic series given a1=9, d=3, and n=14.

A. 797
B. 399
C. 1594
D. 798

Answer 1

B) 399

Explanation:

We want to find the sum of the arithmetic series given that:

`a_1=9, \, d = 3, \text{ and } n = 14`

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:

`\displaystyle S = (n)/(2)\left(a + x_n\right)`

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:

`x_n=a+d(n-1)`

Since the initial term is 9 and the common difference is 3:

`x_n=9+3(n-1)`

Then the 14th or last term is:

`\displaystyle x_(14)=9+3((14)-1)=9+39=48`

Then the sum of the first 14 terms is:

`\displaystyle \begin{aligned} S_(14) &= (14)/(2)\left(9+48\right) \\ \\ &= 7(57) \\ \\ &= 399\end{aligned}`

Our answer is B.