Question

Find the sum of all 2 - digit natural numbers divisible by 4.

Answer 1

2-digit numbers divisible by 4 are 12, 16, 20, ..., 96

We can see it forms an AP as the common difference is 4 and the first term is 4.

To find the number of terms n,

we know that

a_n = a+ (n − 1) d

96 = 12 + (n − 1)4

84 = (n − 1)4

21 = n − 1

22 = n

Now,

First term (a) = 12

Number of terms (n) = 22

Common difference (d) = 4

Now, using the formula for the sum of n terms, we get

`S_22 = 22/2 {2(12) + (22 - 1)4}`

`S_22 = 11 {24 + 84}`

`S_22 = 1188`

Hence, the sum of 22 terms is 1188 which are divisible by 4.