The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers?
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Wrong answer
You're welcome! I'm here to assist with your questions and provide some humor along the way. Let's see if I can solve this one for you!
To find the greatest of the 11 consecutive positive integers, we need to remember that the sum of consecutive integers can be found by multiplying the average of the first and last integer by the number of integers. In this case, the sum of the 11 integers is 2002.
So, let's call the first integer "x." The sum of the 11 consecutive positive integers can then be expressed as: x + (x+1) + (x+2) + ... + (x+10) = 2002.
Now, we can simplify this equation by using the sum formula for an arithmetic series. The sum of the integers from 1 to n is n(n+1)/2, where n is the number of integers. In this case, n = 11.
So, the equation becomes: 11x + 55 = 2002.
Now, we can solve for x: 11x = 2002 - 55, which gives us 11x = 1947.
Dividing both sides by 11, we get x = 177.
Therefore, the greatest of the 11 consecutive positive integers is x+10, which is 177+10 = 187.
So, the greatest integer is 187. Ta-da!
You're welcome! I'm here to help you find the answer to your question. Let's work through it step by step.
To find the greatest of the 11 consecutive positive integers, we'll start by finding the average (or mean) of the 11 integers.
The sum of these integers is given as 2002, so to find the average, we'll divide 2002 by 11:
2002 / 11 = 182
Next, we'll identify the middle number in the sequence (which is also the median). Since there are 11 integers, the middle number will be the 6th number in the sequence.
Now, we'll count back 5 numbers from the 6th number to find the first number in the sequence. This will be the greatest of the 11 integers.
Starting from the 6th number (182), we'll count back 5 numbers:
182 - 5 = 177
So, the greatest of the 11 consecutive positive integers is 177.
If you have any further questions, feel free to ask!
Wow, this helped me sooooo much, thank you!!! Keep making posts like this.
a 1 = first number
a 2 = a 1 + 1 = second number
a 3 = a 1 + 2 = third number
a 4 = a 1 + 3 = fourth number
a 5 = a 1 + 4 = fifth number
a 6 = a 1 + 5 = sixth number
a 7 = a 1 + 6 = seventh number
a 8 = a 1 + 7 = eighth numer
a 9 = a 1 + 8 = ninth number
a 10 = a 1 + 9 = tenth number
a 11 = a 1 + 10 = eleventh number
a 1 + a 2 + a 3 + a 4 + a 5 + a 6 + a 7 + a 8 + a 9 + a 10 + a 11 = 2002
a 1 + a 1 + 1 + a 1 + 2 + a 1 + 3 + a 1 + 4 + a 1 + 5 + a 1 + 6 + a 1 + 7 + a 1 + 8 + a 1 + 9 + a 1 + 10 = 2002
11 a 1 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 2002
11 a 1 + 55 = 2002
11 a 1 = 2002 - 55
11 a 1 = 1947 Divide both sides by 11
a 1 = 1947 / 11
a 1 = 177
a2 = a 1 + 1 = 177 + 1 = 178
a 3 = a 1 + 2 = 177 + 2 = 179
a 4 = a 1 + 3 = 177 + 3 = 180
a 5 = a 1 + 4 = 177 + 5 = 181
a 6 = a 1 + 5 = 177 + 5 = 182
a 7 = a 1 + 6 = 177 + 6 = 183
a 8 = a 1 + 7 = 177 + 74 = 184
a 9 = a 1 + 8 = 177 + 8 = 185
a 10 = a 1 + 9 = 177 + 9 = 186
a 11 = a 1 + 10 = 177 + 10 = 187
a 1 + a 2 + a 3 + a 4 + a 5 + a 6 + a 7 + a 8 + a 9 + a 10 + a 11 =
177 + 178 + 179 + 180 + 181 + 182 + 183 + 184 + 185 + 186 + 187 = 2002
The greatest is eleventh number:
a 11 = 187