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# Maths C1 HELP!!!!!!!!!!!!! ARITHMETIC PROGRESSIONS

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1. An AP is given by k, 2k/3, k/3, 0, . . ..
(i) Find the sixth term.
Using a+(n-1)d I get k+5d but I don't know how to solve d.
2. (Original post by CounTolstoy)
An AP is given by k, 2k/3, k/3, 0, . . ..
(i) Find the sixth term.
Using a+(n-1)d I get k+5d but I don't know how to solve d.
I do not think there is a way of solving for k (without more information, though I am not doubting that you have provided the full question) but I think that they want the answer in terms of k.
3. (Original post by CounTolstoy)
An AP is given by k, 2k/3, k/3, 0, . . ..
(i) Find the sixth term.
Using a+(n-1)d I get k+5d but I don't know how to solve d.
d is the distance between each term. In an arithmetic progression, d is constant.
4. (Original post by SeanFM)
I do not think there is a way of solving for k (without more information, though I am not doubting that you have provided the full question) but I think that they want the answer in terms of k.
You're right, I don't actually have to solve k but I don't know how to give the answer in terms of k without finding the value of d. This means I must figure out the common difference but I see no pattern!
5. (Original post by CounTolstoy)
You're right, I don't actually have to solve k but I don't know how to give the answer in terms of k without finding the value of d. This means I must figure out the common difference but I see no pattern!
There is a pattern there but you also don't need to spot a pattern - as above, an artihmetic progression has a constant difference term 'd' (hence you use the formula for the nth term, a + (n-1)d because the first term is a, the second term you add d on (so it's a+d), the third term you add d to the second term (so it's a + d + d = a +2d).. and so on.
6. (Original post by CounTolstoy)
An AP is given by k, 2k/3, k/3, 0, . . ..
(i) Find the sixth term.
Using a+(n-1)d I get k+5d but I don't know how to solve d.
d is the common difference between each term in the AP. So what's the difference between 2k/3 and k and k/3 and 2k/3? That's your value of d. *

For example, 5, 8, 11, 14, 17... is an AP and d=3.*
7. (Original post by kingaaran)
d is the common difference between each term in the AP. So what's the difference between 2k/3 and k and k/3 and 2k/3? That's your value of d. *

For example, 5, 8, 11, 14, 17... is an AP and d=3.*
I understand d is a constant...but I don't understand the pattern in the sequence . k ----> 2k/3 is just multiply by 2 and divide by three but that is definitely incorrect. I'm sorry but I can't understand this. Can you please explain?
8. (Original post by CounTolstoy)
I understand d is a constant...but I don't understand the pattern in the sequence . k ----> 2k/3 is just multiply by 2 and divide by three but that is definitely incorrect. I'm sorry but I can't understand this. Can you please explain?
Common difference is . That is all you can do. So .
9. (Original post by SeanFM)
There is a pattern there but you also don't need to spot a pattern - as above, an artihmetic progression has a constant difference term 'd' (hence you use the formula for the nth term, a + (n-1)d because the first term is a, the second term you add d on (so it's a+d), the third term you add d to the second term (so it's a + d + d = a +2d).. and so on.
Right so, the first term will be a+(n-1)d
The second term will be a+d+(n-1)d, is that correct, Sean?
If so, may I just ask why we are multiplying the result of (n-1) by d?
My initial question remains though: how can I obtain the value of d? I don't know what sort of pattern there is, progressing from a single k to a 2k/3 to k/3.
10. (Original post by CounTolstoy)
Right so, the first term will be a+(n-1)d
The second term will be a+d+(n-1)d, is that correct, Sean?
If so, may I just ask why we are multiplying the result of (n-1) by d?
My initial question remains though: how can I obtain the value of d? I don't know what sort of pattern there is, progressing from a single k to a 2k/3 to k/3.
Not quite - if you reread my previous post you will see that the second term is a+2d rather than a + d + (n-1)d, and I have shown you how/why you multiply n-1 by d (where n is the term number, eg with a + (n-1)d, the first term (case where n=1), the term is a + (1-1)d = a + 0d = a.

I've also answered your second question in my previous post so I am not sure what to say without repeating anything.
11. (Original post by B_9710)
Common difference is . That is all you can do. So .
How did you solve the common difference? Is there a method to it? I also don't understand how that IS the common difference because if we substitute your proposed value of d in the form a+(n-1)d, we get:
k+(5)(-k/3) = k-5k/15
I am quite sure I have done something wrong somewhere but I am very confused. I am not doubting your answer, I just want an explanation with regards to how you found d and why d = -k/3.
12. (Original post by CounTolstoy)
How did you solve the common difference? Is there a method to it? I also don't understand how that IS the common difference because if we substitute your proposed value of d in the form a+(n-1)d, we get:
k+(5)(-k/3) = k-5k/15
I am quite sure I have done something wrong somewhere but I am very confused. I am not doubting your answer, I just want an explanation with regards to how you found d and why d = -k/3.
To find the common difference subtract the first term from the second term.
13. (Original post by CounTolstoy)
How did you solve the common difference? Is there a method to it? I also don't understand how that IS the common difference because if we substitute your proposed value of d in the form a+(n-1)d, we get:
k+(5)(-k/3) = k-5k/15
I am quite sure I have done something wrong somewhere but I am very confused. I am not doubting your answer, I just want an explanation with regards to how you found d and why d = -k/3.
Yeah you have. Is 5*(k/3) = 5k/15?
14. (Original post by kingaaran)
Yeah you have. Is 5*(k/3) = 5k/15?
no its 5k/3

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15. (Original post by HFancy1997)
no its 5k/3

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Of course it is - I know that, lol. I'm questioning their working because the OP was asking what he did wrong...
16. (Original post by HFancy1997)
no its 5k/3

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17. (Original post by kingaaran)
Of course it is - I know that, lol. I'm questioning their working because the OP was asking what he did wrong...
I just realised my mistake. Thanks very much for pointing that out.
18. (Original post by B_9710)
To find the common difference subtract the first term from the second term.
Ooooooh I never knew that. So 2k/3 -k = k/3 = d. Am I correct?
19. (Original post by CounTolstoy)
Ooooooh I never knew that. So 2k/3 -k = k/3 = d. Am I correct?
Yes. It makes sense because . In fact the common difference in general is .

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