Chapter 1.1, Problem 14PPSE

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 $a_n=5n+5$ .

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 $10$ .

The number of tiny squares in second figure is $15$ .

The number of tiny squares in third figure is $20$ .

The number of tiny squares in fourth figure is $25$ .

Therefore, the sequence is:

  $10,15,20,25,\mathrm{...}$

Here,

  $a=10$ and $d=5$

Therefore, the $n$ th term will be:

  $a_n=a+\left(n-1\right)d$

Substitute the values:

  $\begin{array}{c}{a}_n=10+\left(n-1\right)\left(5\right)\\ a_n=10+5n-5\\ a_n=5n+5\end{array}$

Therefore, The expression for the number of tiles or circles in the $n$ th figure is $a_n=5n+5$ .