#### nicholasbacon

##### New member

- Joined
- Jan 12, 2010

- Messages
- 5

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.

Multiple Answers Are:

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

will someone please help me?!?

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.