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 ${\displaystyle \frac{n\left(n+1\right)\left(2n+1\right)}{6}}$

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
$\Rightarrow {\displaystyle \frac{n\left(n+1\right)\left(2n+1\right)}{6}}$ . Here the value of n is 10.
Therefore, their sum of squares is ${\displaystyle \frac{10\left(10+1\right)\left(2\times 10+1\right)}{6}}={\displaystyle \frac{10\times 11\times 21}{6}}={\displaystyle \frac{2310}{6}}=385$
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 $1+4+9+16+25+36+49+64+81+100=385$