Question

How many even numbers from 2 added to get sum is 110?
How many even numbers from 2 added to get sum is 110?

Answer 1

Answer:

The sum of all even numbers from 2 to 100 as an AP whose first term is 2 and the common difference is 2. First find the number of terms between 2 and 100. For that

Tn = 100 = a + (n-1)d = 2 +(n-1)*2, or

50 = 1+n-1 = n, SO Tn = 50

Sn = (n/2)[2a+(n-1)d] = (50/2)[2*2 + (50–1)*2]

= 25[4+98]

= 25*102

=2550. Answer