- #1
fluppocinonys
- 19
- 1
Homework Statement
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 |.
Homework 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]
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?