Consider an arithmetic progression whose first term is and common difference is

MATHEMATICS · Multi-part · CBSE · Mathematics · Arithmetic Progressions · Arithmetic Progressions

Problem

Consider an arithmetic progression whose first term is

a

and common difference is

d

. Prove the general formula for the sum of the first

n

terms when

n

is an even positive integer. (a) Write the expression for the

n

th term of the progression. (b) Show that the sum of the first

n

terms is

S_n=\frac{n}{2}\bigl[2a+(n-1)d\bigr].