(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An arithmetic progression has n terms and a common difference of d. Prove that the difference between the sum of the last k terms and the sum of the first k terms is | (n-k)kd |.

2. Relevant equations

[tex]\begin{array}{l}

{S_n} = \frac{n}{2}\left[ {2{a_1} + \left( {n - 1} \right)d} \right] \\

{u_n} = {a_1} + \left( {n - 1} \right)d \\

\end{array}[/tex]

3. The attempt at a solution

I have no idea how to apply the "first 3 terms" and "last 3 terms" into the equation...

Do I use [tex]{u_n}[/tex] as last term, and subsequently [tex]{u_{n - 1}}[/tex], [tex]{u_{n - 2}}[/tex] for last second and third term?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Arithmetic Progression

**Physics Forums | Science Articles, Homework Help, Discussion**