The Recycling Department of a fast food chain is planning to have a Christmas Tree Making Contest in preparation of the upcoming Holiday Season. Part of the contest mechanics is to collect soft drinks tin cans and build a Christmas Tree out of the tin cans. If you want to join the contest and plan to have 40 tin cans in the bottom row and one tin can fewer in each successive row. How many tin cans are there in your Christmas Tree?

so you want

40+39+38+...+1 or 1+2+3+...+39+40

a = 1, d = 1 for n=40

sum(40) = (40/2)(first + last)
= 20(1+40)
= 820

To find out how many tin cans are there in your Christmas Tree, you need to determine the total number of tin cans in each row and then sum them up.

In this case, the number of tin cans in each row decreases by one. The bottom row has 40 tin cans, and each successive row has one tin can fewer.

The number of tin cans in each row can be represented by a sequence. We can start by listing the number of tin cans in each row:

40, ?, ?, ?, ...

To find the total number of tin cans, we need to add up all the numbers in the sequence.

We know that the bottom row has 40 tin cans, so the first term in the sequence is 40. The second term will have one fewer tin can because it's one row above the bottom row. The third term will have two fewer tin cans, and so on.

The sum of an arithmetic sequence can be calculated using the formula:

Sum = n/2 * (first term + last term)

Where "n" represents the number of terms in the sequence.

To determine the number of terms in the sequence, we need to find the common difference. The common difference is the amount by which the terms differ from one another. In this case, the common difference is -1 because each term has one fewer tin can compared to the previous term.

To find the number of terms, we can use the formula for the nth term of an arithmetic sequence:

nth term = first term + (n-1) * common difference

Since we want to find the term where the number of tin cans is 0 (the topmost row), we set the nth term equal to 0 and solve for n:

0 = 40 + (n-1) * -1

Rearranging the equation, we get:

-n + 1 = -40

Simplifying further:

n = 41

So, there are 41 terms in the sequence, which means the top row has 0 tin cans. Now, we have all the information we need to calculate the total number of tin cans in the Christmas Tree.

Using the formula for the sum of an arithmetic sequence:

Sum = n/2 * (first term + last term)

Sum = 41/2 * (40 + 0)

Sum = 41/2 * 40

Sum = 820

Therefore, there are a total of 820 tin cans in your Christmas Tree.