Chapter 11, Problem 4CR

To determine

To calculate: The correct option which shows value of arithmetic means of $-2$ and $13$

  $\begin{array}{l}a.1,10\\ b.2,9\\ c.3,8\\ d.4,7\end{array}$

Answer to Problem 4CR

The correct option is (c).

The value of arithmetic means of $-2$ and $13$ is $3$ and $8$ .

Explanation of Solution

Given information:

  $\begin{array}{l}{a}_1=-2\\ a_4=13\end{array}$

Formula used:

Arithmetic sequence: $a_n=a+\left(n-1\right)d$

Common difference: $d=\frac{a_1+a_4}{2}$

Calculation:

Consider the following sequence:

  $\begin{array}{l}d=\frac{13-\left(-2\right)}{3}\\ d=5\end{array}$

Apply the formula:

  $\begin{array}{l}{a}_n=a+\left(n-1\right)d\\ a_2=\left(-2\right)+\left(2-1\right)5\\ a_2=3\end{array}$

Put the value of $a_2$ in formula:

  $\begin{array}{l}{a}_n=a+\left(n-1\right)d\\ a_2=\left(-2\right)+\left(3-1\right)5\\ a_3=8\end{array}$

The correct option is (c).

The value of arithmetic means of $-2$ and $13$ is $3$ and $8$ .