Question

Which if the following summation notations represent this series?

Answer 1

E.

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:

`(35)/(5)=i`

`7=i`

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

So the answer is choice E.