Question

If the number of consecutive odd integers whose sum can be expressed as ${50}^2-{13}^2$ is k then k, can be

• A. 33
• B. 35
• C. 37
• D. 39

Answer 1

Answer: (C)

37

Sum of odd $n$ consecutive numbers $n^2$

$\therefore (1+3+5\dots \dots (2n-1\left)\right)=n^2$

where $n$ represents the number of terms.

$\therefore {50}^2=1+3+5\dots 99=50terms$

$\therefore {13}^2=1+3+5\dots 25=13terms$

$\therefore {50}^2-{13}^2$$=(1+3+5\dots 99)-(1+3+5\dots 25)=(27+29\dots 99)=37terms.$