Question

What is the sum of the consecutive even numbers from 2 to 110

Answer 1

consecutive even numbers between 2 to 110 is 2, 4, 6, 8, 10, 12, ......110

Let number of terms = n
then, use
formula,
Tn = a + (n-1)d
where a is first and d is the common difference of AP
here,
a = 2,
Tn = 110
d = 2
so,
110 = 2 + 2(n-1)
108 = 2(n-1)
55 = n

now,
use the formula ,
Sn = n/2 { first term + nth term}
= 55/2 { 2 + 110}
= 55(112)/2
= 55 × 56
= 3080 ( answer )

Answer 2

sum of the consecutive even numbers from 2 to 110 = sum of first 55 even numbers.

Sum of first n even numbers = n ( n + 1)

Sum of first 55 even numbers = 55(56) =3080.

Hence, the sum of the consecutive even numbers from 2 to 110 is 3080