If not, then one approach (which fits the title of the thread more accurately, I suppose) is to prove this result by induction:
and then once you have, set that equal to 364 and solve.
]]>No: this is not an arithmetic series. The terms form the sequence of triangular numbers, whose nth term is (which you can also write as , though I prefer the former).You have been asked to find the value of such that That last term is the nth term of the sequence . Notice that if , then . Similarly taking gives you , and so on. So what you actually want to do is find the value of such that:I know that 1, 3, and 6 are the result of arithmetic series with the starting value 1 and the difference 2, thus that sum can be written as
+ + + ... + = 364.
Do you know how to do that?
]]>What I did:
I know that 1, 3, and 6 are the result of arithmetic series with the starting value 1 and the difference 2, thus that sum can be written as