Pattern Recognition

Question

The number of bricks in the bottom row of a brick wall is 49. The next row up from the bottom contains 47 bricks, and each

 

subsequent row contains 2 fewer bricks than the row immediately below it. The number of bricks in the top row is 3. If the wall

 

is one brick thick, what is the total number of bricks in the wall?

Answer 1

This really boils down to the sum of the arithmetic sequence:

 

49+47+45+43+ ... + 5+3.

 

Use the formula S_n = n/2 (a₁ + a_n). Since there are (49-1)/2 =24 rows of bricks (you may need to ask about that),

 

use n = 24, a₁ = 49, a₂₄ = 3:

 

S₂₄ = 24/2 (49+3) = 624.

 

The wall has 624 bricks. You could check this by adding up all of the numbers, but why bother?