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# Reposted because the answer I got last time was incorrect and didn't explain how they got there.

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(a) Compute the sum

\(101^2 - 97^2 + 93^2 - 89^2 + \cdots + 5^2 - 1^2.\)

(b) Compute the sum

\((a +(2n+1)d)^2- (a + (2n)d)^2 +(a + (2n-1)d)^2 - (a+(2n-2)d)^2 + \cdots + (a+d)^2 - a^2.\)

Repost of this one:

https://web2.0calc.com/questions/need-help_24323

Apr 21, 2020
edited by Melody  Apr 21, 2020

#1
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Apr 21, 2020
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No. This is the first question I have posted to this site.

I am asking for help with a proper explanation so that I may understand the problems and their solutions better.

I am under the "guest" profile because I haven't made an account and I don't feel the need to.

If you don't want to answer, that is fine, but I would appreciate if you could at least point me in the right direction.

Thank you.

Guest Apr 21, 2020
#3
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*by first, I mean the first question I have posted to this site, though I have asked it once before on a different post.

Guest Apr 21, 2020
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Apr 21, 2020
#5
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https://web2.0calc.com/questions/need-help_24323

Guest Apr 21, 2020
#6
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a - The answer of 5,304 in NOT wrong! It just wasn't explained to you how they arrived at the answer. What is the difference between 1st term and 2nd term? 101 - 97 =4. Each term after the first is 4 LESS than the previous term.So, you get: 101 - 4 =97 - 4 =93 - 4 =89 - 4=85.........etc. all the way down to 5 - 4 =1. And then each term is "squared":

101^2 =10,201 - 97^2 =9,409 + 93^2 =8,649......etc.
This is the "closed form formula" that generates each term of your sequence:  (-1)^(n+1)*(105 - 4*n)^2, where n=1 to 26.

And this is what you get, when you expand your sequence: [10201, -9409, 8649, -7921, 7225, -6561, 5929, -5329, 4761, -4225, 3721, -3249, 2809, -2401, 2025, -1681, 1369, -1089, 841, -625, 441, -289, 169, -81, 25, -1]
Sum them up on your calculator term by term and you should get =5,304.
I hope you understand it now. Good luck to you.

Guest Apr 21, 2020
edited by Guest  Apr 21, 2020
#7
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Oof. I did not understand the problem at all then. Thank you for clearing that up! Sorry about that.

Guest Apr 21, 2020
#10
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Take the difference in squares and then sum them up as an arithmetic sequence as follows:

All you need are the first term [101^2 - 97^2]=792 and the last term [5^2 - 1^2] =24 and the number of terms = 26 and the common difference = 4

Sum =[F + L] / D x N, where F=First term, L=Last term, D=Common difference, N=number of terms.

Sum =[792 + 24] / 4 x 26
=[816 / 4] x 26
= 204 x 26
= 5,304

Guest Apr 21, 2020
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You can look at this question as follows:

Apr 21, 2020
#9
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Here's the answer to part b:

You should check this carefully, as I did it rather hurriedly!

Apr 21, 2020