Question

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

The correct option is C 37

Sum of odd n consecutive numbers $n^2$

Therefore, $1+3+5+...+2n-1=n^2$ where n represents the number of terms.

Therefore, ${50}^2=1+3+5+...+99$ = 50 terms

${13}^2=1+3+5+...+25$ = 13 terms

Therefore,

${50}^2-{13}^2=27+29+....+99$ = 37 terms