Mathematics Question Thread

[iktimal]

Hello,
Can someone please assist me in finding Tn of this series?
5-2+10-8+15-32

[RuiAce]

Hello,
Can someone please assist me in finding Tn of this series?
5-2+10-8+15-32

From what it looks like, this looks like two sequences clumped together into one. For each odd value, we have \( T_{2n-1} = 5n \) and \(T_{2n} = -2 \times 4^{n-1} \).

(Note that this is because the odd terms form an A.P. with common difference 5, and the even terms form a G.P. with common ratio 4.)

Note that writing out \(S_n\) would therefore be a bit awkward.

[iktimal]

From what it looks like, this looks like two sequences clumped together into one. For each odd value, we have \( T_{2n-1} = 5n \) and \(T_{2n} = -2 \times 4^{n-1} \).

(Note that this is because the odd terms form an A.P. with common difference 5, and the even terms form a G.P. with common ratio 4.)

Note that writing out \(S_n\) would therefore be a bit awkward.

Hi Rui,
Well actually the next part of the question asks for the sum of the first 20 terms of the series. How would I do it using these equations?
Would I look for the sum of the first 20 terms for the AP and GP then add them together?

[RuiAce]

Hi Rui,
Well actually the next part of the question asks for the sum of the first 20 terms of the series. How would I do it using these equations?

You can think of it like this. 10 of those terms will be "odd terms", namely position 1, 3, 5, ..., 19. The other terms will be the even terms.

So you can add: {sum of 10 terms in an AP with first term 5 and common difference 5} + {sum of 10 terms in a GP with first term -2 and common ratio 4}. This would be equivalent to \(\boxed{ \frac{10}{2} \left[2(5) + (10-1)(5) \right]+ \frac{-2\left(4^{10}-1\right)}{4-1}}\).

[iktimal]

You can think of it like this. 10 of those terms will be "odd terms", namely position 1, 3, 5, ..., 19. The other terms will be the even terms.

So you can add: {sum of 10 terms in an AP with first term 5 and common difference 5} + {sum of 10 terms in a GP with first term -2 and common ratio 4}. This would be equivalent to \(\boxed{ \frac{10}{2} \left[2(5) + (10-1)(5) \right]+ \frac{-2\left(4^{10}-1\right)}{4-1}}\).

Oh I see now, thank you very much 

[jamonwindeyer]

Help me plz...


I love you! <3

[jamonwindeyer]

Help me plz...


I love you! <3

weird...

[emilyyyyyyy]

Hi!

Just a general question; how much of the prelim course do we have to know? and should I be actively studying it?

[r1ckworthy]

Hi!

Just a general question; how much of the prelim course do we have to know? and should I be actively studying it?

Hi Emily,

I assume you will be doing the HSC this year, so you're still part of the old syllabus. Yes, you will have to know ALL of the preliminary course. As mentioned by RUIace below, you will still have to know all of the preliminary course for the new syllabus as well. In the 2-Unit maths HSC, you will be tested on  topics such as plane geometry, trig functions, real functions etc, which you have learned last year. These types of questions typically come in the earlier questions of the HSC 2-Unit exam, although they do have a slight chance to come up in more difficult questions.

In terms of studying actively, the best thing you can do is to go through HSC papers. When I accelerated the course last year, we haven't covered that much of Yr12 topics when it was time for our half yearlies. Unlike others, I went through and answered the HSC papers from 2012-17, skipping the questions that I didn't know. This advice came from a teacher, and it really helped me. This is the best way you can learn. Attempt a paper from start to finish and check the answers if you are having a hard time and see if you have learned that topic yet. If not, just keep going. If you are struggling with a topic (eg. trig functions), go back to your textbook and do more questions. That is the best way to study for mathematics (or what I found really helpful).

Hope that helped!!

[emilyyyyyyy]

Thank you!!

[RuiAce]

Hi Emily,

I assume you will be doing the HSC this year, so you're still part of the old syllabus. Yes, you will have to know the most important bits of the preliminary course. x

Remark: For both the old and new syllabuses, you're expected to know all of the preliminary/Year 11 course.

[r1ckworthy]

Remark: For both the old and new syllabuses, you're expected to know all of the preliminary/Year 11 course.

Thanks, I'll correct my answer soon.

[shaynec19]

Hi anyone that can answer my question...
Just struggling with this question atm. Keep seeming to get the wrong answer.
"Find the equation of the tangent to the curve y=lnx at the point (2,ln2)."
VVVV simple question, I just can't see what I'm doing wrong.
Cheers

[MB_]

Hi anyone that can answer my question...
Just struggling with this question atm. Keep seeming to get the wrong answer.
"Find the equation of the tangent to the curve y=lnx at the point (2,ln2)."
VVVV simple question, I just can't see what I'm doing wrong.
Cheers

Would you be able to post your working so we can see where you're getting stuck?

[shaynec19]

Yep Sure,
I have differentiated lnx to get 1/x. This is my gradient right?
I then used the point gradient formula with the x&y values.