Explanation:
A Given,
Let the numbers be \(\mathrm{a}-\mathrm{d}, \mathrm{a}, \mathrm{a}+\mathrm{d}\) are in A.P.
\(\therefore \quad \mathrm{a}+\mathrm{d}+\mathrm{a}+\mathrm{a}-\mathrm{d} =21\)
\(3 \mathrm{a} =21\)
\(\mathrm{a} =7\)
Again, \((\mathrm{a}-\mathrm{d})(\mathrm{a}+\mathrm{d})=45\)
\(a^2-d^2=45\)
\((7)^2-d^2=45\)
\(49-d^2=45\)
\(d= \pm 2\)
\(\therefore \quad\) Numbers are \(5,7,9\) or \(9,7,5\)
\(\therefore \quad\) Product of three numbers \(=5 \times 7 \times 9=315\)
