Solution:
we have been asked to find the sum of the even integers between 21 and 45.
The even integers between 21 and 45 is
22, 24, 26,28, 30, 32, 34, 36,38, 40, 42,44.
its forming an arithmetic progression with
first term=22=a
number of term=12=n
common difference=24-22=2=d
The sum can be found using the formula
[tex] S_n=\frac{n}{2}[2a+(n-1)d]\\ [/tex]
Substitute the values in the above formula we get
[tex] S_{12}=\frac{12}{2}[2*22+(12-1)2]\\
\\
S_{12}=6[44+22]\\
\\
S_{12}=6*66\\
\\S_{12}=396\\ [/tex]
