Question 3

We can see a pattern when we add odd numbers.

Step 1 — Finding the pattern

Look at the dots in the picture. The first odd number is 1. It makes a square of size $1 \times 1$.

$1 = 1 \times 1$

$\boxed{1}$

Now, let us add the next odd number, which is 3. We add 3 dots to the 1 dot. This makes a square of size $2 \times 2$.

$1 + 3 = 4$

$4 = 2 \times 2$

$\boxed{4}$

Next, let us add the odd number 5. We add 5 dots to the 4 dots. This makes a square of size $3 \times 3$.

$1 + 3 + 5 = 9$

$9 = 3 \times 3$

$\boxed{9}$

Let us add the odd number 7. We add 7 dots to the 9 dots. This makes a square of size $4 \times 4$.

$1 + 3 + 5 + 7 = 16$

$16 = 4 \times 4$

$\boxed{16}$

We can see a clear pattern. The sum of the first 'n' odd numbers is $n \times n$.

Step 2 — Sum of first 10 odd numbers

We need to find the sum of the first 10 odd numbers. The first 10 odd numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19. Using our pattern, 'n' is 10. The sum will be $10 \times 10$.

$1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 10 \times 10$

$= 100$

$\boxed{100}$

Answer

The sum of the first 10 odd numbers is 100.