Question

The sum of five consecutive odd numbers is 220.
find the greatest of the five numbers.​

Answer 1

Answer:

${(n + 1)}^{2} + {(n + 3)}^{2} + {(n + 5)}^{2} \\ + {(n + 7)}^{2} + {(n + 9)}^{2} = 220 \\ 5 {n}^{2} + 165 + 50n = 220 \\ 5 {n}^{2} + 50n - 55 = 0 \\ {n}^{2} + 10n - 11 = 0 \\ {n}^{2} + 11n - n - 11 = 0 \\ n(n + 11) - 1(n + 11) = 0 \\ (n + 11)(n - 1) = 0$

So,

n = 1

The numbers are,