Question

Find the sum of n terms of the ap a a+b a+2b.......a+(n-1)d

Answer 1

.n2+B.n ................................................................. (1)

Note that the sum will always be a quadratic polynomial without constant term. From (1) we get S(1)=A+B....................... (2)

S(2)=4A+2B .......................(3)

S(3)=9A+3B ......................(4)

where S(n) is the sum of the first n terms.

Hence a(1)=A+B .........................................................(5),

a(2)=S(2)−S(1)=3A+B..........................(6)

∴ the common difference is 2A.

A short cut method : To find the common difference, take the double of the coefficient of n2.

( ie The coefficient of n in the derivative of S(n) with respect to n.)