Question

The sum of the three numbers in A.P is $21$ and the product of the first and third number of the sequence is $45$. What are the three numbers?

• A. $3,7,$ and $11$
• B. $9,7,$ and $5$
• C. $3,9,$ and $15$
• D. Both $A$ and $B$
• E. None of these

Answer 1

Answer: (B)

$9,7,$ and $5$

Let the three numbers in A.P be $a-d,a,a+d.$
Then,

$\begin{array}{cc}a-d+a+a+d& =21\\ 3a& =21\\ a& =7\end{array}$

And,

$\begin{array}{cc}(a-d)(a+d)& =45\\ a^2-d^2& =45\\ (7{)}^2-d^2& =45\\ 49-d^2& =45\\ d^2& =4\\ d& =\pm 2\end{array}$

Hence, the numbers are $5,7$ and $9$ when $d=2$ and $9,7$ and $5$ when $d=-2$.

In both cases, numbers are the same.