Question

what is the sum of all odd integers between 10 and 28

Answer 1

$\underline{\textsf{To find:}}$

$\textsf{Sum of all odd integers between 10 and 28}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\textsf{Sum of all odd integers between 10 and 28}$

$\mathsf{=11+13+15+.......+27}$

$\textsf{This can be written as}$

$\mathsf{=(1+3+........+9)+11+13+15+.......+27-(1+3+........+9)}$

$\mathsf{=(1+3+..............+27)-(1+3+........+9)}$

$\mathsf{=(\dfrac{m+1}{2})^2-(\dfrac{n+1}{2})^2}$

$\mathsf{=(\dfrac{27+1}{2})^2-(\dfrac{9+1}{2})^2}$

$\mathsf{=(14)^2-(5)^2}$

$\mathsf{=196-25}$

$\mathsf{=171}$

$\underline{\textsf{Answer:}}$

$\textsf{Sum of all odd integers between 10 and 28 is 171}$