Thread: consecutive odd integers

The sum of 3 consecutive odd integers is k. In terms of k, what is the sum of the 2 smaller of these integers?

Do I need to use substitution somehow?? (The answer given is but can't figure it out..)

Originally Posted by mjoshua

The sum of 3 consecutive odd integers is k. In terms of k, what is the sum of the 2 smaller of these integers?

Do I need to use substitution somehow?? (I know it's gonna be but can't figure it out..)

k - (largest odd integer).

If you post the whole question you might get an answer that's more suitable for your purpose.

Originally Posted by mjoshua

The sum of 3 consecutive odd integers is k. In terms of k, what is the sum of the 2 smaller of these integers?

Do I need to use substitution somehow?? (I know it's gonna be but can't figure it out..)

Let n be the middle odd integer so we have



as Mr F said, you'll need to expand

That IS the entire question (it's taken out of my book as is)

Originally Posted by mjoshua

The sum of 3 consecutive odd integers is k. In terms of k, what is the sum of the 2 smaller of these integers?

Do I need to use substitution somehow?? (The answer given is but can't figure it out..)

Perhaps the idea of an arithmetic sequence can help us.

Let be the middle number so that our sequence is

For 3 consecutive odd numbers the mean will be equal to the middle number. Hence

is the middle number.

Hence the smaller number is: .

The question is asking us to find the sum of the two smaller numbers:



which is the book's answer

Originally Posted by e^(i*pi)

Perhaps the idea of an arithmetic sequence can help us.

Let be the middle number so that our sequence is

Why can we use this sequence though? (Should it be a consecutive integer odd sequence? If you try n = 0, or n = 2 it's not completely odd.

Originally Posted by mjoshua

Why can we use this sequence though? (Should it be a consecutive integer odd sequence? If you try n = 0, or n = 2 it's not completely odd.

Neither 0 nor 2 are odd integers.

If you think about an arithmetic sequence it is defined as there being a common difference between each term. For consecutive odd integers this is 2. n is 2 more than n-2 and n+2 is 2 more than n.

If we try and hence

and sure enough

But instead of declaring "n" just an odd integer, shouldn't we use a sequence like 2n + 1 so that no matter what you put it for n (even or odd) you still get an odd integer? (so it's more inclusive?)

Originally Posted by mjoshua

But instead of declaring "n" just an odd integer, shouldn't we use a sequence like 2n + 1 so that no matter what you put it for n (even or odd) you still get an odd integer? (so it's more inclusive?)

You have been given the solution on a platter in post #5. Now it's your job to take some ownership of that solution and modify it if you want to express the odd numbers in the way you describe.

Originally Posted by mjoshua

But instead of declaring "n" just an odd integer, shouldn't we use a sequence like 2n + 1 so that no matter what you put it for n (even or odd) you still get an odd integer? (so it's more inclusive?)

Hello Mjoshua,
I was going to reply to this post yesterday but decided that eipi had adequately answered it I passed.Today you appear confused.Here is the way I would have replied.

Three cons odd integers are n, n+2, n+4, the sum of these =k
Solution of this equation n=k-6/3. The sum of the first two is 2n+2 and thisbecomes 2/3k-2 when you insert the value of n in terms of k.

bjh

Originally Posted by mr fantastic

You have been given the solution on a platter in post #5. Now it's your job to take some ownership of that solution and modify it if you want to express the odd numbers in the way you describe.

And I can see that solution. I was just asking a simple question, if was to better to instead create a "proof" for n as any positive or negative integer that covers all cases. I guess you missed that..