Answer
Sum of odd integers between 30 and 54 = 31 + 33 + 35 + 37 +........+ 53 = 504
Work Step by Step
Sum of odd integers between 30 and 54 = 31 + 33 + 35 + 37 +........+ 53
First term $a_{1}$ = 53
Last term $a_{l}$= 31
Common difference (d)= 2
Number of terms = $\frac{(Last term - first term)}{difference (d)}$ + 1
Number of terms (n) = $\frac{(53 - 31)}{2}$ + 1 = $\frac{22}{2}$ + 1 = 11 + 1 = 12
Sum of n terms = $\frac{n}{2}$($a_{1}$ + $a_{n}$)
= $\frac{n}{2}$($a_{1}$ + $a_{l}$)
= $\frac{12}{2}$(53 + 31)
= 6$\times$84 = 504
Sum of odd integers between 30 and 54 = 31 + 33 + 35 + 37 +........+ 53 = 504
