Chapter 8.1, Problem 4PSA

a

To determine

To find:The fourth proportion for given set of terms i.e. 1,2, and 3.

Answer to Problem 4PSA

The fourth term is 6.

Explanation of Solution

Given information

Terms given are 1, 2, 3

Formula used

Product of means = Product of extremes

Calculation

Let us assume the fourth term is x.

Then we have

1, 2, 3, x

Terms can be written as

1:2::3:x

Using formula,

Product of means = product of extremes

  $\begin{array}{l}1\times \text{ x=2}\times \text{3}\\ \text{x=6}\end{array}$

Thus, fourth term is 6

b

To determine

To find:The fourth proportion for given set of terms i.e. $\frac{1}{2},3,4$ .

Answer to Problem 4PSA

The fourth term is 24

Explanation of Solution

Given information Terms given are $\frac{1}{2}$ , 3, 4

Formula used Product of means = Product of extremes

Calculation Let us assume the fourth term is x.

Then we have

  $\frac{1}{2}$ : 3:: 4: x

On using formula

Product of means = Product of extremes

  $\begin{array}{l}\frac{1}{2}\times x=3\times 4\\ x=2\times 3\times 4\\ x=24\end{array}$

Hence, fourth term is 24

c

To determine

To find:The fourth proportion for given set of terms i.e. a, b, 5.

Answer to Problem 4PSA

The fourth term is $\frac{5b}{a}$

Explanation of Solution

Given information

Terms given are a, b, 5

Formula used

Product of means = Product of extremes

Calculation

Let us assume the fourth term is x.

Then we have

a, b , 5, x

Terms can be written as

a:b::5:x

Using formula,

Product of means = product of extremes

  $\begin{array}{l}a\times x=b\times 5\\ x=\frac{b\times 5}{a}\\ x=\frac{5b}{a}\end{array}$

Thus, fourth term is $\frac{5b}{a}$