Prove that the sum of n terms of an AP in which first term acommon dif

1.	Prove that the sum of n terms of an AP in which first term acommon difference d and last termI, is given by
Answer» Derivation for the Sum of Arithmetic Progression,SS=a1+a2+a3+a4+...+an S=a1+(a1+d)+(a1+2d)+(a1+3d)+...+[a1+(n−1)d]→ Equation (1) S=an+a(n−1)+a(n−2)+a(n−3)+...+a1 S=an+(an−d)+(an−2d)+(an−3d)+...+[an−(n-1)d]→ Equation (2) Add Equations (1) and (2)2S=(a1+an)+(a1+an)+(a1+an)+(a1+an)+...+(a1+an) 2S=n(a1+an) S=n(a1+an)/2.

Prove that the sum of n terms of an AP in which first term acommon difference d and last termI, is given by

Answer»

Derivation for the Sum of Arithmetic Progression,SS=a1+a2+a3+a4+...+an

S=a1+(a1+d)+(a1+2d)+(a1+3d)+...+[a1+(n−1)d]→ Equation (1)

S=an+a(n−1)+a(n−2)+a(n−3)+...+a1

S=an+(an−d)+(an−2d)+(an−3d)+...+[an−(n-1)d]→ Equation (2)

Add Equations (1) and (2)2S=(a1+an)+(a1+an)+(a1+an)+(a1+an)+...+(a1+an)

2S=n(a1+an)

S=n(a1+an)/2.