Question

Find the sum of the first 8 odd numbers?

Answer 1

Hint: In the given question, we are asked to write the sum of 8 odd numbers and we know that all those numbers which are not divisible by 2 are known as the odd numbers. We can find the sum by writing all odd numbers till 8 or else we can use the formula to find that.

Complete step-by-step solution:
As per the question, we need to find the sum of the first 8 odd numbers. Now, we must know that the odd numbers are all those numbers which are not completely divisible by 2 and hence give the remainder as 1. So, if we need to find the first 8 odd numbers, what we need to do is divide every number starting from 1 by 2 and find all the odd numbers.
Also, if we find any odd number then adding 2 to that number or subtracting 2 from that number will also give the odd number different from the taken odd number.
Now, the first 8 odd numbers are 1,3,5,7,9,11,13,15 and we know that it is forming an arithmetic progression where the common difference d is 2 and the first term is 1 and last term is 15.
Now, we know that sum is given by $S=\dfrac{n}{2}\left[ 2a+\left( n-1 \right)d \right]$ and substituting the values we get,
$\begin{align}
  & S=\dfrac{n}{2}\left[ 2a+\left( n-1 \right)d \right] \\
 & S=4\left[ 2+7\times 2 \right] \\
 & S=4\times 16 \\
 & S=64 \\
\end{align}$
Therefore, by this the sum of the first 8 odd numbers is 64.
Also, we know that the sum of n odd numbers is equal to ${{n}^{2}}$ . Therefore, according to the question n=8 therefore, the sum of 8 odd numbers is 64.
Hence, the sum of first 8 odd numbers is 64.

Note: Some we get confused whether 1 is odd or not like prime or composite numbers. So, 1 is also an odd number and 0 is considered to be an even number although it does not add any value to the sum but for the knowledge, we must know this. Rest in the question sum is asked in which there are very less chances of error until and unless it is any calculation mistake.