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?

624

Step-by-step explanation:

The sequence is 49, 47, 45, ..., 7, 5, 3. This is an arithmetic sequence, because the difference between terms is the same.

The sum of the first n terms of an arithmetic sequence is:

S = n/2 (a₁ + an)

where a₁ is the first term and an is the nth term.

Here, we know that a₁ = 49 and an = 3. But we need to find what n is. To do that, we use definition of an arithmetic sequence:

an = a₁ + (n-1) d

where d is the common difference (in this case, - 2)

3 = 49 + (n-1) (-2)

2 (n-1) = 46

n - 1 = 23

n = 24

So there are 24 terms in the sequence.

The sum is:

S = 24/2 (49 + 3)

S = 12 (52)

S = 624

There are 624 bricks in the wall.