Finding an Unknown Sequence

Date: 3/31/96 at 13:59:19
Subject: Math Problem
From: John Sylvester

I cannot figure out where to start on this Series and Sequences 
question.

1+3x+6(x)(x)+10(x)(x)(x)+15(x)(x)(x)(x)+. . .

Can you help me?

Sincerely, Cory Sylvester

Date: 3/31/96 at 20:23:20
From: Doctor Jodi
Subject: Re: Math Problem

Hi there!  The first thing I usually try to do in the sequence is to 
determine the pattern.  There are two patterns here:

the coefficients:

1, 2, 3, 6, 10, 15

the "x's"

1, x, x^2, x^3, x^4

I think you'll find the second pattern pretty easily.  For the first, 
here's  a hint:  find the difference between each two terms in the 
sequence. Do you see a pattern?

Good luck and let us know if you need more help!

-Doctor Jodi,  The Math Forum