Question

What is the sum of numbers from 40 to 300

Answer 1

Let the numbers from 40 to 300 form an Arithmetic progression or a sequence.

The first term is 40 and the common difference is 1.

Let 300 be the n^th term.

We will need to use the formula , a_n = a + (n - 1)d , where a_n is n^th term, a = first term, d = difference

300 = 40 + (n - 1) * 1

==> 300 = 40 + n - 1

==> 300 = 39 + n

==> 300 - 39 = n

Hence n = 261

Hence 300 is 261^th term.

The formula for finding sum of n terms of arithmetic progression is,

S₂₆₁ = 44370

Hence sum of numbers from 40 to 300 is 44370.

Hope this will help you.