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