# Arithmetic Series/Sequence

#### nicholasbacon

##### New member
I've ran into an Arithmetic Series/Sequence problem that I can not figure out.

The only information the problem gives me is as follows:
Sum=1390
First Term=3
Last Term=136

What they want is the first three numbers in the sequence, the first one has already been given to me->3.

A. 3, 10, 17
B. 3, 23, 43
C. 3, 36 1/3, 70
D. 3, 69 1/2, 136
E. 3, 139, 1251

I know the answer to the question; A, because the answer is on the worksheet, but I need to know how to get that answer.

I know the following equations for sequence and series;

To find a missing term using the numbers existing in the arithmetic sequence:
Tn=To+(n-1)d
To=1st Term
n=Term number to find (i.e. sequence=1,3,_,7-the blank is represented as n=3)
d=Ratio of progression (i.e. in the above sequence; "d" would be 2)

So what I can plug in for this would be:
To=3
n=2 (or 3 because I need both terms in the end, but the answer to one would give me the other)
d=?
Tn=3+(2-1)d
Tn=3+d
Tn-3=d

This is correct for A., B. and E. so I feel my formula is lacking a definitive answer.
I know that I can double-check by plugging the difference between terms in the answers given
But that would just confirm that I'm doing the math correctly, not that I have the right answer
Example: Tn=3+(2-1)7
Tn=10
VS
Tn=3+(2-1)20
Tn=23

So that gets me nowhere :-(
I'm so confused

I could continue the sequences and see if I get 136 eventually but I feel like if I didn't have given answers then
I would be at a loss with what I know how to do as of right now

I also know that
To find the sum of a certain number of terms in an arithmetic series:
Sum=n(To+Tn)/2
n=number of terms being included for the sum (i.e. 1,3,5,7. To find the sum of all terms n=4)
To=1st Term
Tn=Last Term

But double-checking my answer with this equation is irrelevant with the information I'm given.

I have a gut feeling that I need both equations to find the answer, but I can't seem to figure out how to integrate them to do it.

Staff member

#### nicholasbacon

##### New member
Yes I did duplicate a post, it was because I wasn't sure if this post belonged in beginning algebra or intermediate/advanced. So i apologize.