Finding the first 40 positive odd integers

In summary, the solution to finding the sum of the first 40 positive odd integers is to use the formula ##1 + 2(n - 1)##, where n is the index of the odd number. This results in the 40th positive odd integer being 79.
  • #1
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I have the following problem: What is the sum of the first 40 positive odd integers?

I look at the solution, and it says that "The sum of the first 40 positive odd integers is ##1 + 3 + 5 + \dotsm + 77 + 79##. And then it goes on with the solution.

My question is, how do I find that 79 is the 40th positive odd integer? Do I have to just write them all down until I get to the 40th one?
 
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  • #2
Mr Davis 97 said:
I have the following problem: What is the sum of the first 40 positive odd integers?

I look at the solution, and it says that "The sum of the first 40 positive odd integers is ##1 + 3 + 5 + \dotsm + 77 + 79##. And then it goes on with the solution.

My question is, how do I find that 79 is the 40th positive odd integer? Do I have to just write them all down until I get to the 40th one?
The first odd positive integer is 1. The second one is 1+2. The third one is 1+2+2. How many times you need to add 2 to get 40 terms?
(What kind of sequence is 1, 3, 5. 7, ... ? What is the N-th term of that sequence?)
 
  • #3
ehild said:
The first odd positive integer is 1. The second one is 1+2. The third one is 1+2+2. How many times you need to add 2 to get 40 terms?
(What kind of sequence is 1, 3, 5. 7, ... ? What is the N-th term of that sequence?)
Ah, so I can just create an arithmetic sequence ##1 + 2(n - 1)##, where n is the index of the odd number. So when I substitute 40 I just get 1 + 2(39) = 79! Awesome, thanks.
 

1. What are the first 40 positive odd integers?

The first 40 positive odd integers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, and 81.

2. How can I find the first 40 positive odd integers?

To find the first 40 positive odd integers, you can start with the number 1 and add 2 to it repeatedly until you reach 40 numbers. This will give you the sequence 1, 3, 5, 7, 9, 11, and so on, up to 81.

3. What is the pattern in the sequence of the first 40 positive odd integers?

The pattern in the sequence of the first 40 positive odd integers is that each number is 2 more than the previous number. This is because odd numbers are always 2 apart from each other, starting with 1 as the first odd number.

4. Why are there only 40 positive odd integers and not more?

There are only 40 positive odd integers because we are starting with the number 1 and counting up to 81. Since 81 is the 40th odd number, we will have 40 numbers in total.

5. Are there any other ways to find the first 40 positive odd integers?

Yes, there are other ways to find the first 40 positive odd integers. For example, you can start with the number 0 and add 2 to it repeatedly until you reach 40 numbers. This will give you the sequence 0, 2, 4, 6, 8, 10, and so on, up to 78. You can also use a formula such as 2n+1, where n represents the position of the number in the sequence, to find the first 40 positive odd integers.

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