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Question
Find the sum of all 2 - digit natural numbers divisible by 4.
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Solution
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
an = 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.
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