Question

Derive mathematically Sn=n/2(2a+(n-1)d)

Answer 1

Let there be an Ap
a,a+d, a+2d ........ a+(n-1)d

Sum = a + a+d + a +2d + .... + a+(n-1)d

Also reversing the order we get
Sum = a+(n-1)d + a+(n-2)d +...... a

adding first and second
2* sum = 2a+(n-1)d + 2a +(n-1)d +...... + 2a+(n-1)d

since there are n terms

2*sum = n(2a+(n-1)d)

sum = n/2 (2a +(n-1)d)