Find the sum of 3 digit natiral numbers which are multiples of 11

1.	Find the sum of 3 digit natiral numbers which are multiples of 11
Answer» Three digits numbers that are divisible by 11 are :-110, 121, 132,.............., 990Clearly ,above sequence is an A.P.Here,\xa0a (First term)\xa0= 110d (common difference)\xa0= 11an = 990We know that, in A.P.an\xa0= a + (n - 1)dOr, 990 = 110 + (n - 1)\xa0{tex}\\times{/tex}\xa011Or, 990 = 110 + 11n - 11Or, 990 = 99 + 11nOr, 891 = 11nOr, n = 81Also,\xa0Sn\xa0 =\xa0{tex}\\frac n 2{/tex} (a + an)Or, S81\xa0= {tex}\\frac{{81}}{2}(110 + 990){/tex}Or, S81 = 81\xa0{tex}\\times{/tex}550Or, S81 = 44550.

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