Question

What is the sum of all odd natural numbers from 11 to 31 (both inclusive)?

Answer 1

please find the attachment

Answer 2

Answer: The sum of all odd natural numbers from 11 to 31 is 231

Step-by-step explanation:

The numbers are 11, 13, 15 , ............. 31

Now It forms an AP where first term a= 11 , common difference d= 13-11 = 2 , last term l = 31

Now $l=a_n= a+(n-1)d\\\\\Rightarrow 31= 11+(n-1)2\\\\\Rightarrow 20= (n-1)2\\\\\Rightarrow n= 11$

Now as we know the sum of AP is given by

$S_n=\dfrac{n}{2} (a+l)\\\\\Rightarrow S_{11}=\dfrac{11}{2} (11+31)= 231$

Hence, the sum of all odd natural numbers from 11 to 31 is 231