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  • 17. While adding the first fewa candidate missed one of theanswer as 177. Wh.first few continuous natural numbers.one of the numbers and wrote theras 177. What was the number missed?(a) 11(b) 12(c) 13(d) 14?

17. While adding the first fewa candidate missed one of theanswer as 177. Wh.first few continuous natural numbers.one of the numbers and wrote theras 177. What was the number missed?(a) 11(b) 12(c) 13(d) 14?

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The;formula;for;the;sum;of;the;first;n;natural;numbers;is; fracn(n+1)2\* Let;the;number;missed;be=k\* fracn(n+1)2-k=177\* n^2+n-2k=354\*n^2+n-354=2k\* ecause k geqslant1,;so;2k geqslant2 \*so,;n^2+n-354geqslant 2\* n^2+n-352geqslant 0\* In;integers;the;inequality;has;solutions\*n = -20,-21,-23,... ;;and ;n = 19, 20, 21,...\*Substituting;n=19;in\*fracn(n+1)2-177=k\* 19(19+1)2-177=k\* 190-177=k\*13=k\* herefore missing;number;is;13

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Deependra Verma

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