Find the no. Of three digit natural no. Which are divisible by 11

1.	Find the no. Of three digit natural no. Which are divisible by 11
Answer» Three digit natural numbers are 100,101,102.....,998,999. From which,\xa0multiples of 11 are 110, 121, 132, ...., 990.so,this forms an AP 110,121....,990.\xa0where, first term ({tex}a {/tex})=110 and common difference({tex}d{/tex})=121-110=11, last term({tex}l{/tex}) = 990..Let,\xa0{tex}l = {a_n} = a + (n - 1)d{/tex}{tex}\\therefore 990 = 110 + (n - 1) \\times 11{/tex}{tex} \\Rightarrow n = 81{/tex}There are 81 three - digit numbers which are divisible by 11.

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