# Mathematic expression

By zugedanit

@zugedanit (1958)

Philippines

February 16, 2007 9:02am CST

Mathematic expression. 1,5,9,13,17 total of first 2 terms: 1+5= 2*3 total of first 3 terms: 1+5+9= 3*5 and so on. then it asks to write down an expression, in n, for the total. i don't understand how to work out this expression.

2 responses

@cubbycubz (27)

• Philippines

23 Mar 07

zugedanit,just try this:
in your given mathematical expression, 1,5,9,13,17, what is n? simply as this: 1+n=5, 5+n=9, 9+n=13, and 13+n=17. let the value of n=4,substitute. you will obtain those numbers. 1+4=5, 5+4=9, 9+4=13 and 13+4=17. got it?

@AJMSmith (113)

•

17 Feb 07

The terms being summed are 4-3,2*4-3,3*4-3 etc for the Nth term you have N*4-3.
Since the terms are linear in N (no N^2 or higher powers), the sum must be quadratic, that is of the form S(N) = aN^2 + bN + c. Then the difference between the sum of the first N terms and the first N+1 terms is
S(N+1) - S(N) = a((N+1)^2 - N^2) + b((N+1) - N) + c(1-1) = a(2N + 1) + b = 2aN + (a+b)
Since we know that this is just the N+1st term it equals (N+1)*4-3 = 4N + 1.
This gives a = 2 and b = -1. S(N) = 2N^2 - N + c.
Since S(1) = 1, 2-1+c=1 so c=0.
S(N) = 2N^2-N = N(2N-1).
A simelar method will work for any sequence sum.
Work out a formula for the Nth term
Evaluate the difference for the right polynomial