The average of 5 consecutive odd numbers is 27. What is the product of the first and the last number?

Solution(By Examveda Team)

Let first odd number = a
Five odd number = a, a + 2, a + 4, a + 6, a + 8
= 5a + 2(1 + 2 . . . 4)
= 5a + 2$$\frac{{\left( 4 \right)\left( 5 \right)}}{2}$$
= 5a + 20
According to the question,
$$\frac{{5a + 20}}{5}$$ = 27
a + 4 = 27
a = 23
First number = 23
Last number = 23 + 8 = 31
Product of first and last number = 23 × 31 = 713

Alternate:
\[\begin{array}{*{20}{c}} {23}&{25}&{\boxed{27}}&{29}&{31} \\ \downarrow &{}& \downarrow &{}& \downarrow \\ {{\text{First Number}}}&{}&{{\text{Average}}}&{}&{{\text{Last Number}}} \end{array}\]
Average is middle term if common difference between them is same.
Product = 23 × 31 = 713