Chapter 1.1, Problem 13PPSE

Solution

The expression for the number of tiles or circles in the $n$ th figure.

The expression for the number of tiles or circles in the $n$ th figure is $a_n=2n$ .

Given:

  

Formula Used:

The formula of Arithmetic sequence is:

  $a_n=a+\left(n-1\right)d$

Where,

  $a\to$ First term

  $d\to$ Common difference

  $n\to$ Number of terms

  $a_n\to$

  $n$ th term

Calculation:

The number of tiny squares in first figure is $2$ .

The number of tiny squares in second figure is $4$ .

The number of tiny squares in third figure is $6$ .

The number of tiny squares in fourth figure is $8$ .

Therefore, the sequence is:

  $2,4,6,8,\mathrm{...}$

Here,

  $a=2$ and $d=2$

Therefore, the $n$ th term will be:

  $a_n=a+\left(n-1\right)d$

Substitute the values:

  $\begin{array}{c}{a}_n=2+\left(n-1\right)\left(2\right)\\ a_n=2+2n-2\\ a_n=2n\end{array}$

Therefore, The expression for the number of tiles or circles in the $n$ th figure is $a_n=2n$ .