Question

Which if the following summation notations represent this series?

Answer 1

Answer:

E.

Step-by-step explanation:

Let's look at the sequence:

$3,8,13,\cdots$

The sequence has a common difference. We say it has a common difference because 8-3 has the same value as 13-8.

The common difference is what these differences are equal which is 5.

The sequence is therefore linear or arithmetic (same thing).

So it has form $y=mx+b$ where the slope/common difference is 5.

$y=5x+b$

We need to find the $y-$intercept $b$.

The list of points is related to the above sequence:

$(x,y)$

$(1,3)$

$(2,8)$

$(3,13)$

I only need one of these points to find $b$.

Let's use the first one since it has smallest numbers and I don't wish to use the calculator unless I really have to.

$y=5x+b$ with $(x,y)=(1,3)$:

$3=5(1)+b$

$3=5+b$

Subtract 5 on both sides:

$3-5=b$

$-2=b$

So the equation for the set of points is:

$y=5x-2$

Now they are using $i$ instead of x[/tex]:

$a_i=5i-2$

Since all summations begin at $i=1$, then the choices are done to either choice C and choice E.

I need to find how many terms are in the given series. The last number is 33. So what term number is associated with the value 33.

$a_i=5i-2$

$33=5i-2$

Add 2 on both sides:

$35=5i$

Divide both sides by 5:

$\frac{35}{5}=i$

$7=i$

So there are 7 terms and the 7th term is 33.

So the answer is choice E.