Question

The sum of squares of first ten natural numbers is
A. 375
B. 385
C. 475
D. 485

Answer 1

Hint : Natural numbers are the whole numbers except 0 which means they start from 1 till infinity. First ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. We can find the sum of squares of these ten natural numbers using the below mentioned formula by putting n as 10.
Formula used:
Sum of squares of first ‘n’ natural numbers is $\dfrac{{n\left( {n + 1} \right)\left( {2n + 1} \right)}}{6}$

Complete step-by-step answer :
We are given to find the sum of squares of the first ten natural numbers.
Natural numbers are part of the number system which are the positive integers starting from 1 till infinity. There are infinite natural numbers.
The first 10 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.
Sum of squares of first ‘n’ natural numbers is
$\Rightarrow \dfrac{{n\left( {n + 1} \right)\left( {2n + 1} \right)}}{6}$ . Here the value of n is 10.
Therefore, their sum of squares is $\dfrac{{10\left( {10 + 1} \right)\left( {2 \times 10 + 1} \right)}}{6} = \dfrac{{10 \times 11 \times 21}}{6} = \dfrac{{2310}}{6} = 385$
Sum of squares of the first 10 natural numbers is 385. Hence, the correct option is Option B.
So, the correct answer is “Option B”.

Note : Another approach.
The first 10 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.
The square of 1 is ${1^2} = 1$ , the square of 2 is ${2^2} = 4$ , the square of 3 is ${3^2} = 9$ , the square of 4 is ${4^2} = 16$ , the square of 5 is ${5^2} = 25$ , the square of 6 is ${6^2} = 36$ , the square of 7 is ${7^2} = 49$ , the square of 8 is ${8^2} = 64$ , the square of 9 is ${9^2} = 81$ and the square of 10 is ${10^2} = 100$
The sum of squares of first 10 natural numbers will be $1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385$