Find the sum of 3 digit …
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Sia ? 4 years, 8 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
an = 990
We know that, in A.P.
an = 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,
Sn = {tex}\frac n 2{/tex} (a + an)
Or, S81 = {tex}\frac{{81}}{2}(110 + 990){/tex}
Or, S81 = 81 {tex}\times{/tex}550
Or, S81 = 44550.
0Thank You