Question

What is the value of the arithmetic series below?

Answer 1

Answer:

(A)-494

Step-by-step explanation:

Given the arithmetic series

$S_{19}=\sum_{k=1}^{19}4-3k$

The terms in the sequence are:

• When k=1, 4-3k=4-3(1)=1
• When k=2, 4-3k=4-3(2)=-2
• When k=3, 4-3k=4-3(3)=-5

Therefore, the terms in the sequence are: 1, -2, -5, ...

First term, a =1

Common difference, d=-2-1=-3

The sum of an arithmetic series, $S_n=\dfrac{n}{2}[2a+(n-1)d]$

Therefore:

$S_{19}=\dfrac{19}{2}[2(1)+(19-1)(-3)]\\=9.5[2+18*-3]\\=9.5[2-54]\\=9.5*-52\\=-494$

The correct option is A.