Question

Find the sum of all even numbers between 50 and 100 using a formula.

Answer 1

The even numbers strictly between 50 and 100 are: 52, 54, 56, ..., 98.

a = 52

l = 98

d = 2

We use the n^th term formula:

l = a + (n − 1)d

98 = 52 + (n − 1)2

98 − 52 = (n − 1)2

46 = (n − 1)2

`46/2 = (n − 1)`

= 23 = n − 1

23 + 1 = n

n = 24

`S_n = n/2 (a + l)`

`S_24 = 24/2 (52 + 98)`

= 12 × 150

= 1,800