Question

Find the sum of the following numbers without actually adding the number
a) 1+3+5+7+9+11+13+15
b) 1+3+5+7

Answer 1

Sum of first n consecutive odd numbers is $n^2$
In first expression we have 8 consecutive odd tyerms
so we will get answer as $8^2=64$
In second expression we have 4 consecutive odd numbers
so we will get as $4^2=16$