Sequences And Series Ques 52
A pack contains $n$ cards numbered from $1$ to $n$. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is $1224$. If the smaller of the numbers on the removed cards is $k$, then $k-20$ is equal to
(2013 Adv.)
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Answer:
Correct Answer: 52.$(5)$
Solution:
Formula:
An Arithmetic Progression (A.P.):
- Let number of removed cards be $k$ and $(k+1)$.
$\therefore \frac{n(n+1)}{2}-k-(k+1)=1224$
$\Rightarrow \quad n^{2}+n-4 k=2450 \Rightarrow n^{2}+n-2450=4 k$
$\Rightarrow \quad(n+50)(n-49)=4 k$
$\therefore \quad n>49$
Let $\quad n=50$
$\therefore \quad 100=4 k$
$\Rightarrow \quad k=25$
Now $\quad k-20=5$
BETA
