Arithmetic Series/Sequence

[nicholasbacon]

I am brushing up on my algebra/trig/calc skills before going back to school... there is a problem that I have not been able to figure out involving arithmetic sequence and series.

The only information I have is:
Sum=1390
First Term=3
Last Term=136

The question is to find the first three terms

I know the equations tn=to+(n-1)d and Sum=n(to+tn)/2 but when trying to find out the 2 terms following the first with only the sum and the last term in the sum, I can't seem to come up with a formula to do so. I really need help with this thanks!

 

[nicholasbacon]

Also, to add, it is a multiple answer question, the answers include

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, because it is in the worksheet, but I don't know how to get the answer, so that is my problem, thanks.

 

[mmm4444bot]

Hi Nicholas:

I'll use underscores, to indicate subscripts.

You know the following.

Sum of first n terms = n(t_0 + t_n)/2

If you substitute the given values for the sum, t_0, and t_n, you get an equation that you can solve for n (i.e., the number of terms that sum to 1390).

In other words, solve the following for n.

1390 = n(3 + 136)/2

Once you know n, you can use substitution in the other equation to find d.

t_n = t_0 + (n - 1)(d)

Of course, as soon as you find d, you can find any term(s).

t_0 = 3 + 0d

t_1 = 3 + 1d

t_2 = 3 + 2d

t_3 = 3 + 3d

t_4 = 3 + 4d

Et cetera.

Cheers,

~ Mark

 

[nicholasbacon]

Thank you very much, I was on the right track. I did think to solve for n in the series equation, though, I was under the impression that the variable n was represented by different numbers in both equations (i.e., Tn=To+(n-1)d---n=Term # to find, and in series; n=number of terms in the sequence). So unfortunately I did not go with my gut instinct due to that fact. Now that I am aware of that ability, I am more confident in using the formulas, so again I thank you.