Ask Singapore Homework?
Upload a photo of a Singapore homework and someone will email you the solution for free.
Question
secondary 3 | E Maths
3 Answers Below
Anyone can contribute an answer, even non-tutors.
Help
Date Posted: 4 years ago
Views: 212
Each term is n(n-3) where n represents the order of the term
For example ,
1st term , T1 = 1(1 - 3) = 1 x -2 = -2
2nd term, T2 = 2(2 - 3) = 2 x -1 = -2
3rd term, T3, = 3(3 - 3) = 3 x 0 = 0
4th term, T4 = 4(3 - 4) = 4 x -1 = -4
For example ,
1st term , T1 = 1(1 - 3) = 1 x -2 = -2
2nd term, T2 = 2(2 - 3) = 2 x -1 = -2
3rd term, T3, = 3(3 - 3) = 3 x 0 = 0
4th term, T4 = 4(3 - 4) = 4 x -1 = -4
So T27 = 27(27 - 3) = 27 x 24 = 648
T50 = 50(50 - 3) = 50 x 47 = 2350
T50 = 50(50 - 3) = 50 x 47 = 2350
Now, we know each term is n(n-3) = n² - 3n
Similarly, we make k² - 144 into the form of k² - 3k and equate it to the latter
k² - 144 = k² - 3(48)
k² - 3(48) = k² - 3k
Comparing coefficients,
k = 48
Since k² - 3k = k(k - 3),
k(k - 3) = 48(48 - 3) = 48 x 45 = 2160
So this term is the 48th term and T48 = 2160
Similarly, we make k² - 144 into the form of k² - 3k and equate it to the latter
k² - 144 = k² - 3(48)
k² - 3(48) = k² - 3k
Comparing coefficients,
k = 48
Since k² - 3k = k(k - 3),
k(k - 3) = 48(48 - 3) = 48 x 45 = 2160
So this term is the 48th term and T48 = 2160
I just want to point out that there are more than one value of k. In fact, n can equal to 143,48, 20, 15, 3 which gives the entire solution set of k as {142, 48, 22, 18,12}
yup. k can be negative as well since the question has no restrictions.
Then again, the most intuitive one for this question would be 48 since the student would just manipulate the expression to look like n² - 3n
Then again, the most intuitive one for this question would be 48 since the student would just manipulate the expression to look like n² - 3n
See 3 Answers
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
This is some useful notes for you, IN CASE the question requires you to find Tn, or did not provide you the formula. In order to use this, the number pattern MUST be a quadratic pattern (refer to comment section).
Date Posted:
4 years ago
Example of a quadratic pattern:
1, 1, 2, 4, 7, 11, 16, ...
For this number pattern, we realised that the first set of 'jumps' are not the same as it goes like this:
+0, +1, +2, +3, +4, +5, ...
However, we find that all the 'jumps' have the common thing - they are added by 1 (+1).
In short, a quadratic pattern is something like these two qns - first set of 'jumps' are inconsistent, second set of 'jumps' are consistent.
1, 1, 2, 4, 7, 11, 16, ...
For this number pattern, we realised that the first set of 'jumps' are not the same as it goes like this:
+0, +1, +2, +3, +4, +5, ...
However, we find that all the 'jumps' have the common thing - they are added by 1 (+1).
In short, a quadratic pattern is something like these two qns - first set of 'jumps' are inconsistent, second set of 'jumps' are consistent.
But in this case, the question provides you with the Tn. So it's a lot more easier to just find T27 and T50. But it's good to keep this in mind if you encounter this kind of question in the future. :)
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
Since we find Tn earlier (refer to notes), we can find the value of k. Let me know if you have any difficulties in understanding this concept of quadratic patterns. :)
Date Posted:
4 years ago
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
This is for part a
Date Posted:
4 years ago
360 Tutoring Program