Chapter 3.6, Problem 15HP

To determine

To find: a sequence of number with the first number $4$ .

Answer to Problem 15HP

The required equation is $2n+2$ and the sequence of the number is $4,6,8,\mathrm{10......}$

Explanation of Solution

Given information:

The first number of the sequence is $4$

Consider the first number of the sequence as $4$ and the difference between the numbers as $2$ .

Consider the nth term of the sequence.

  $a_n=a_1+\left(n-1\right)d$

Substitute $4$ for $a_1$ and $2$ for $d$ in the above equation.

  $\begin{array}{c}{a}_n=4+\left(n-1\right)2\\ =4+2n-2\\ =2n+2\end{array}$

The equation $2n+2$ represents the sequence of the pattern of numbers.

Now, substitute $1$ for $n$ in the above equation.

  $\begin{array}{c}2n+2=2\times 1+2\\ =4\end{array}$

Substitute $2$ for $n$ in the above equation.

  $\begin{array}{c}2n+2=2\times 2+2\\ =6\end{array}$

Substitute $3$ for $n$ in the above equation.

  $\begin{array}{c}2n+2=2\times 3+2\\ =8\end{array}$

Substitute $4$ for $n$ in the above equation.

  $\begin{array}{c}2n+2=2\times 4+2\\ =10\end{array}$

Hence, the required equation is $2n+2$ and the sequence of the number is $4,6,8,\mathrm{10......}$