Quadratic expressions & equations

by Tom

The sum of the 1st n positive integers is given by 1/2n(n + 1).

a)Given that the sum 14 + 15 + 16 +.... + K is 539.

i)form a quadratic equation in terms of k.
ii) find value of k.

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Sep 30, 2015
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by: Anonymous

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Jul 20, 2011
by: sudhanshu kumar

The sum of the 1st n positive integers is given by (1/2)*n(n + 1).

sum of (k-13)terms of series 14,15.....,k

(1/2)* (k-13)(k+14) =539

=> k^2 + k - 182 = 1078

=> k^2 + k - 1260 =0

now factorize...

k^2 +36k -35k -1260=0

=> (k+36)(k-35)=0

so, k = 35 , because k = -36 not possible.

Jul 19, 2011
by: Andrew Cronie

i) k^2 + k - 1260 = 0

ii) k = 35

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