Series of numbers

• Oct 14th 2008, 11:27 PM
amitr
Series of numbers
I have the following sequence of numbers:

1 3 6 10 15...

It isn't an AP because the difference isn't constant.

It starts in 2, then 3, 4, 5 and so on. Changing 1 each time.

1) Is there a way to know if a number is in this sequence? For instance, is 55 in this sequence? (it is...)

2) What is the difference used to reach some number in the sequence? For instance, the number 55, what is the difference that was used to find it (it is 10, the previous number is 45).

Thanks.
• Oct 15th 2008, 01:55 AM
Ting
Hello

Your answers are correct. Did you get them by writing out the first 10 terms?

The second difference is 1, as you say, so the sequence is related to $\displaystyle \frac{1}{2}n^2$

$\displaystyle \begin {tabular}{c c c c c c} 1 & 2 & 3 & 4 & 5 & n \\ 0.5 & 2 & 4.5 & 8 & 12.5 & (1/2)n squared\\ 1 & 3 & 6 & 10 & 15 &(1/2)n squared + (1/2)n \\ \end {tabular}$

So the sequence is, $\displaystyle \frac{1}{2}(n^2+n)$.

Is that any help?