a catering company has 15 customers orders during its first month. for each month afterward the company has double the number of orders of the previous month. how many orders in total did the company fill in its first year?
looks like a GS where
a = 15
r = 2
n = 12
Sāā = 15(2^12 - 1)/(2-1)
= 61425
but would i have to use the geometric series to find this out
ok thanks you
but when i did it i got 30720
In month 12, there were 30,720 customer's orders.
To find out how many orders the company filled in its first year, we need to calculate the total number of orders for each month and then sum them up.
Let's break it down:
First month: 15 orders
Second month: double the number of orders of the previous month, which is 15 * 2 = 30 orders
Third month: double the number of orders of the previous month, which is 30 * 2 = 60 orders
Fourth month: double the number of orders of the previous month, which is 60 * 2 = 120 orders
And so on...
We can see that the number of orders is doubling each month. This doubling pattern can be represented by the formula 15 * 2^(n-1), where n represents the month number.
Now, since we are interested in finding the total number of orders for the first year, we need to sum up the orders from the first to the twelfth month.
Using the formula, we can calculate the number of orders for each month:
First month: 15 * 2^(1-1) = 15 * 2^0 = 15 orders
Second month: 15 * 2^(2-1) = 15 * 2^1 = 30 orders
Third month: 15 * 2^(3-1) = 15 * 2^2 = 60 orders
...
Twelfth month: 15 * 2^(12-1) = 15 * 2^11
Finally, we can calculate the total number of orders for the first year by summing up the monthly orders:
Total number of orders = 15 + 30 + 60 + ... + (15 * 2^11)
This sum can be calculated using various methods such as the geometri
One way to solve this problem is simply to keep doubling the numbers.
1 - 15
2 - 30
3 - 60
4 - 120
5 - 240
etc.
Be sure to add your numbers together to find the total orders for the year.