Question

Express 169 as the sum of 13 consecutive odd natural numbers.

Answer 1

Step 1: Given Data

In the question, they have asked us to find whether the sum of 13 consecutive numbers is 169 or not

which means we need to prove that sum of 13 consecutive numbers is 169.

the 13 consecutive odd numbers are

$1,3,5,7,9,11,13,15,17,19,21,23,25$

Step 2: Sum of 13 odd numbers

$$\begin{gathered} =1+3+5+7+9+11+13+15+17+19+21+23+25 \\ =(1+25)+(3+23)+(5+21)+(7+19)+(9+17)+(11+15)+13 \\ =26+26+26+26+26+26+13 \\ =(6x26)+13 \\ =156+13 \\ =169 \end{gathered}$$

Hence the sum of 13 consecutive odd numbers is 169