Progressions

What is the sum of the following series?

- 64, - 66, - 68, …… , - 100

  1. - 1458
  2. - 1558
  3. - 1568
  4. - 1664
  5. None of the above

Solution

The series is Arithmetic Progression with

First term = -64

Last term = -100

Common difference = -2

Tn = a + (n-1)d

-100 = -64 + (n-1)*(-2)

n-1 = 36/2 = 18

n = 19

This series has 19 negative numbers, where all the numbers in the series is 2 less than previous number.

Sum = n/2 [a+l]

= 19/2 [- 64 - 100] = - 1558

The correct option is B.