Chapter 12, Problem 16STP

To determine

To find: Number of squares in the tenth step.

Answer to Problem 16STP

Number of squares in tenth step is $a_{10}=22$

Explanation of Solution

Given information:

Number of squares in first step $=4$

Number of squares in first step $=6$

Number of squares in first step $=8$

Concept:

In arithmetic series

  $n^{th}$ term is calculated by the formula

  $a_n=a+\left(n-1\right)d$

Where

  $a$ is the first term of the series.

  $d$ represents common difference

  $n$ represents the which term we need to calculate

Given

Number of squares in first step $=4$

Number of squares in first step $=6$

Number of squares in first step $=8$

This follows arithmetic series as

  $4,6,8,\mathrm{....}$

First term $=a=4$

Common difference $=d=6-4=8-6=2$

As we need to find number of squares in tenth step

  $n=10$

On substituting values in above formula

We get

  $\begin{array}{l}{a}_n=a+\left(n-1\right)d\\ \Rightarrow a_{10}=4+\left(10-1\right)2\\ \Rightarrow a_{10}=4+\left(9\right)2\\ \Rightarrow a_{10}=4+18\\ \Rightarrow a_{10}=22\end{array}$

Therefore,

Number of squares in tenth step is $a_{10}=22$