the-first-n-even-numbers-are-known-if-one-number-is-deleted-then-the-average-of-remaining-numbers-is-2582-50-find-the-value-of-deleted-number-

Question Number 78979 by jagoll last updated on 22/Jan/20

the first n even

numbers are known . if one number

is deleted then the average

of remaining numbers is \frac{2582}{50} .

find the value of deleted number .

Commented by mr W last updated on 22/Jan/20

t h e 51 n u m b e r s a r e 2, 4, 6, \dots 102

t h e d e l e t e t e n u m b e r i s 70

Commented by jagoll last updated on 22/Jan/20

sir please explain me

Commented by mr W last updated on 22/Jan/20

n e v e n n u m b e r s : 2 (1 + 2 + \dots + n) = n (n + 1)

d e l e t e d n u m b e r : 2 m w i t h m ⩽ n

\frac{n (n + 1) - 2 m}{n - 1} = \frac{2582}{50} = \frac{1291 k}{25 k}

n (n + 1) - \frac{1291}{25} (n - 1) = 2 m ⩽ 2 n

n^{2} - \frac{1316}{25} n + \frac{1291}{25} ⩽ 0

\Rightarrow 1 ⩽ n ⩽ 51

\Rightarrow 1 ⩽ k ⩽ 2

k = 1 : \Rightarrow n = 26 \Rightarrow n o i n t e g e r m

k = 2 : \Rightarrow n = 51 \Rightarrow m = 35 \Rightarrow s o l u t i o n

Commented by jagoll last updated on 22/Jan/20

thanks you lot sir

Facebook Tweet Pin