URGENT HELP NEEDED!!! Proof by induction

Hi guys. Could anyone please help me to solve this question?? It's sort of urgent

Prove by Induction:

Sum of terms of an arithmetic sequence
Sn = n/2(2a + (n-1)d)

Thank you muchos!

Do you know how to start? How would you usually do an induction?

I usually start with n= 1 , then assume for n = k , and finish with n = k + 1 but I got stuck at the start with this one.

Well okay, when n = 1, $S_1 = \frac{1}{2}(2a_1 + 0d) = \frac{1}{2}(2a_1) = a_1$ which is obviously true as the sum of the first 1 terms is just equal to the first term.

Now, you assume n=k is correct, so assume:

$S_k = \frac{k}{2}(2a_1 + (k-1)d)$

is true.

Then you get $S_{k+1} =$
Fill in the right hand side, bearing in mind you know what the sum of the first k terms is equal to (you've assumed it's true).

Also remember the formula $a_n = a_1 + (n-1)d$.