#### Question

The average of 5 consecutive odd numbers is 21. Find the smallest odd number.

Question

The average of 5 consecutive odd numbers is 21. Find the smallest odd number.

Using Arithmetic Progression:

An arithmetic progression is a sequence of numbers where each term is obtained by adding a constant value to the previous term.

Let x be the smallest odd number, and let d be the common difference.

Then, the other 4 odd numbers will be x+d, x+2d, x+3d, and x+4d.

We can use the formula for the sum of the first n terms of an arithmetic progression to obtain (5/2)(2x+4d) = 21*5.

Simplifying this equation and substituting x+d = x+2 - x, we get x = 17, which is again the smallest odd number.

Using Algebra:

Let x be the smallest odd number.

Then, the other 4 odd numbers will be x+2, x+4, x+6, and x+8.

We can now write the equation (x + x+2 + x+4 + x+6 + x+8)/5 = 21 and solve for x. The solution is x = 17.