(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?

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# Homework Help: Arithmetic Progression

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