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Question
Find the sum of three-digit natural numbers, which are divisible by 4.
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Solution
The three-digit natural numbers divisible by 4 are
100, 104, 108, ......, 996
The above sequence is an A.P.
∴ a = 100, d = 104 – 100 = 4
Let the number of terms in the A.P. be n.
Then, tn = 996
Since tn = a + (n – 1)d,
996 = 100 + (n – 1)(4)
∴ 996 = 100 + 4n – 4
∴ 996 = 96 + 4n
∴ 996 – 96 = 4n
∴ 4n = 900
∴ n = `900/4`
∴ n = 225
Now, `S_n = n/2 (t_1 + t_n)`
∴ `S_225 = 225/2 (100 + 996)`
= `225/2 (1096)`
= 225 × 548
= 123300
∴ The sum of three-digit natural numbers, which are divisible by 4 is 123300.
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