find the sumof all three digit number which is divisible by 13

1.	find the sumof all three digit number which is divisible by 13
Answer» According to question the three-digit numbers which are divisible by 13 are 104, 117, 130, 143,.…… 938.This forms\xa0an AP in which a = 104, d = (117 – 104) = 13 and\xa0l = 938 (last term)Let the number of terms be n\xa0Then Tn\xa0= 938{tex}\\Rightarrow{/tex}a+(n-1)d=988{tex}\\Rightarrow{/tex}104+(n-1){tex}\\times{/tex}13=988{tex}\\Rightarrow{/tex}13n=897{tex}\\Rightarrow{/tex}n=69Therefore required sum={tex}\\frac{n}{2}{/tex}(a+l)={tex}\\frac{{69}}{2}{/tex}[104+988]=69{tex}\\times{/tex}546=37674Hence, the sum of all three digit\xa0numbers which are\xa0divisible by 13 is equal to 37674.

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