Question

The sum of n terms of an AP in which first term is a, common difference is d and last term is l, is Sn = \(\frac {n}{2}\)(a + l).

(a) True

(b) False

The question was posed to me during an interview for a job.

This interesting question is from Sum of N Terms of Arithmetic Progression in section Arithmetic Progressions of Mathematics – Class 10

Answer 1

Right answer is (a) True

To explain I would say: Consider an AP having n terms in which

First term = a, common difference = d and last term = l.

Then, l = a + (n – 1)d

We may write the given AP as a, a + d, a + 2d …., (l – 2d), (l – d), l

Let Sn be the sum of the first n terms of the AP. Then,

Sn = a + (a + d) + (a + 2d) … + (l – 2d) + (l – d) + l

Writing the above series in reverse order, we get

Sn = (l – 2d) + (l – d) + l … + a + (a + d) + (a + 2d)

Adding the two equations we get,

2Sn = a + l + (a + l) + (a + l) …   n times = n(a + l)

Sn = \(\frac {n}{2}\)(a + l)