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Secondary 1 | Maths
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Date Posted: 2 years ago
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(i) Fifth line :
1 + 3 + 5 + 7 + 9 + 11 = 36 = 6² = (5 + 1)²
(ii) b = 169 = 13² = (12 + 1)²
c = 13, d = 12
Next, notice that for a particular nth line,
number of terms = n + 1
Sum of the terms = (n + 1)²
The last term in the line = 2n + 1
(See the fifth (or 5th) line above for an example. There are 6 terms. Their sum = (5 + 1)² = 6². The last term = 11 = 2 × 5 + 1)
So for d = 12, it means that it is the 12th line and there are 13 terms.
So the last term, a = 2 × 12 + 1 = 24 + 1 = 25
(You can try to check this by adding all the odd numbers from 1 to 25 to convince yourself it's correct)
(iii) No, there will not be. 86868 is an even number. But all the numbers in each line are odd numbers. So it is impossible for an even number like 86868 to appear.
1 + 3 + 5 + 7 + 9 + 11 = 36 = 6² = (5 + 1)²
(ii) b = 169 = 13² = (12 + 1)²
c = 13, d = 12
Next, notice that for a particular nth line,
number of terms = n + 1
Sum of the terms = (n + 1)²
The last term in the line = 2n + 1
(See the fifth (or 5th) line above for an example. There are 6 terms. Their sum = (5 + 1)² = 6². The last term = 11 = 2 × 5 + 1)
So for d = 12, it means that it is the 12th line and there are 13 terms.
So the last term, a = 2 × 12 + 1 = 24 + 1 = 25
(You can try to check this by adding all the odd numbers from 1 to 25 to convince yourself it's correct)
(iii) No, there will not be. 86868 is an even number. But all the numbers in each line are odd numbers. So it is impossible for an even number like 86868 to appear.
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