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

Posted by Uma R 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Three digits numbers that are divisible by 11 are :-
110, 121, 132,.............., 990
Clearly ,above sequence is an A.P.
Here,
a (First term) = 110
d (common difference) = 11
a_n = 990
We know that, in A.P.
a_n = a + (n - 1)d
Or, 990 = 110 + (n - 1) {tex}\times{/tex} 11
Or, 990 = 110 + 11n - 11
Or, 990 = 99 + 11n
Or, 891 = 11n
Or, n = 81
Also,
S_n = {tex}\frac n 2{/tex} (a + a_n)
Or, S₈₁ = {tex}\frac{{81}}{2}(110 + 990){/tex}
Or, S₈₁ = 81 {tex}\times{/tex}550
Or, S₈₁ = 44550.

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