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What is the sum of all 3-digit positive integers divisible by 13?1). 375742). 365743). 376744). 37666

Answer»

Smallest and largest 3 digit number divisible by 13 is 104 and 988.

SUM = 104 + 117 + 130 + 143 + …………+ 988

Using sum of arithmetic series,

$(\frac{n}{2}\left( {FIRST\;TERM + last\;term} \right))$ 

We can write,

988 = 104 + (n -1)13 [nth term = a + (n - 1)d]

$(\Rightarrow {\rm{\;n}} = \frac{{884}}{{13}} + \;1 = 68 + 1 = 69)$

∴ The required sum $(= \frac{{69}}{2}\left( {104 + 988} \right) = \frac{{69}}{2}1092 = 37674)$


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