Question

Thw table shows sums of odd numbers.

n sum of first odd number

1 1

2 1+3=4

3 1+3+5=9

4 1+3+5+7=16

5 1+3+5+7+9=25

1) Write a variable expression for the sum of the first n odd numbers.

2) Use your expression from part (b) to find the sum of the first 100 odd numbers.

Answer 1

$$\begin{gathered} \left(1\right). \\ \mathrm{The}\mathrm{sum}\mathrm{of}\mathrm{first}\mathrm{n}\mathrm{odd}\mathrm{natural}\mathrm{numbers}={\mathrm{n}}^2 \\ \left(2\right). \\ \mathrm{sum}\mathrm{of}\mathrm{first}100\mathrm{odd}\mathrm{natural}\mathrm{numbers}={\left(100\right)}^2=10000 \end{gathered}$$