Question

Help Me fast quick Fast​

Answer 1

To Prove:

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

Proof:

N.B:

a => first term

n => number of terms

d => common difference

The general form of an AP of first n terms

a , a+d ,a+2d ,...

• General term = an = a+(n-1)d

Their sum = a + a +d +a +2d+....+a+(n-1)d

• Sn = a + a + d +a+2d+....+a+(n-1)d ...1

and taking again

• Sn = a+(n-1)d+a+(n-2)d+...+a ....2

On adding 1 and 2

• Sn + Sn = a + a + d + a+ 2d +... + a + (n-1)d + a + (n-1)d + a +(n-2)d+...+a

• 2Sn = 2a+(n-1)d+(2a+(n-1)d+..+(2a+(n-1)d(n times)

• 2Sn = 2a+(n-1)d+(2a+(n-1)d+..+(2a+(n-1)d(n times)

• 2Sn = n× (2a+(n-1)d)

• Sn = (n/2)[2a+(n-1)d]

Hence Proved!!

____________________________