40n^2+9n

Please convert this to the "sum" formula.

Question

40n^2+9n

Please convert this to the "sum" formula.

anonymous · Answer

Any one?

anonymous · Answer

n(40n+9)

myininaya · Answer

a sum formula?

anonymous · Answer

Perhaps he means that is a "term" and he wants to "sum" the terms?

jhonyy9 · Answer

how you have thought it ? - like a*2 +2ab +b*2 = (a+b)*2 - ???

anonymous · Answer

I meant like a "sigma" sum but I couldn't see any way of doing it with the squared term there.

anonymous · Answer

Assuming an arithmetic series of n terms with common difference d and first term a, then the sum is equal to $$\frac{d}{2}n^2+\left(a+\frac{d}{2}\right)n$$
Compare this expression to your answer. Once you have solved for d and a, then the sum will be in the form
$$\sum_{i=1}^n(a+id)$$

anonymous · Answer

Well, yes except that its 40n^2 + 9n....

anonymous · Answer

$$\frac{d}{2}=40$$
$$\left(a+\frac{d}{2}\right)=9$$
Where is the problem?

anonymous · Answer

Set n=1, 2, 3...

49,169,387....

What is the sum Sn?

anonymous · Answer

The original question can be paraphrased as, if I'm not mistaken, "what is the sum that gives the equality
$$\sum_{i=1}^nt_i = 40n^2+9n$$
not "what is
$$\sum_{i=1}^n(40i^2+9i)$$

anonymous · Answer

Well, that's what the original replies were about, what DID he mean and he hasn't returned to tell us so we all just guessing what he might have meant.