Question

If the sum of n terms of a progression be a
quadratic expression in n, show that it is an
A.P.
​

Answer 1

Step-by-step explanation:

Consider the series

a-d, a, a+d , a+2d

Sum of 3 terms will be 3a

3a = 3A² + 3B

a = A² + B

A² + B - a = 0

Sum of 4 terms is 4a + 2d

4a + 2d = 4A² + 4B

d = 2A² + 2B - 2a

d = 2(A² + B - a)

d = 0

Answer 2

Step-by-step explanation:

Answer:

Let the progression be tn

According to the question: tn=an+b

Let us take the consecutive difference: tn−tn−1 =an+b−a(n−1)−b=2a

As the consecutive difference is constant, the sequence is an AP by definition of an AP.