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secondary 2 | Maths
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Pls help me with this qn
Date Posted: 2 years ago
Views: 311
Alternative method : Gauss Pairing
5 + (k - 1) = k + 4
6 + (k - 2) = k + 4
7 + (k - 3) = k + 4
...
...
And so on.
Number of numbers from 5 to (k - 1)
= (k - 1) - 5 + 1
= k - 5
Number of pairs you can make from these numbers = ½(k - 5)
Total in each pair = k + 4 (see above)
Sum of 5 + 6 + 7 + ... + (k - 1)
= Number of pairs × total in each pair
= ½(k - 5)(k + 4)
Since we have two of such sums in the question,
They add up to : (k - 5)(k + 4) = k² - k - 20
Add this to the k in the middle,
Total
= k² - k - 20 + k
= k² - 20
So, k² - 20 = 509
k² = 529
k = √529
(we do not need to consider the negative square root since k is a positive integer)
k = 23
5 + (k - 1) = k + 4
6 + (k - 2) = k + 4
7 + (k - 3) = k + 4
...
...
And so on.
Number of numbers from 5 to (k - 1)
= (k - 1) - 5 + 1
= k - 5
Number of pairs you can make from these numbers = ½(k - 5)
Total in each pair = k + 4 (see above)
Sum of 5 + 6 + 7 + ... + (k - 1)
= Number of pairs × total in each pair
= ½(k - 5)(k + 4)
Since we have two of such sums in the question,
They add up to : (k - 5)(k + 4) = k² - k - 20
Add this to the k in the middle,
Total
= k² - k - 20 + k
= k² - 20
So, k² - 20 = 509
k² = 529
k = √529
(we do not need to consider the negative square root since k is a positive integer)
k = 23
See 1 Answer
done
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Hope this helps
Date Posted:
2 years ago
Alternative for the second part : (since it's a 'hence' question you'll need to use the previous result)
25 + 30 + 35 + ... + 115 + ... + 35 + 30 + 25
= 5 (5 + 6 + 7 + ... + 23 + ... + 7 + 6 + 5)
= 5 (509)
= 2545
25 + 30 + 35 + ... + 115 + ... + 35 + 30 + 25
= 5 (5 + 6 + 7 + ... + 23 + ... + 7 + 6 + 5)
= 5 (509)
= 2545
@j... Yes. This should be the working! Thanks for figure it out :)
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