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arithmetic sequences

Can someone please help me with this question?
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Reply 1
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Notnek
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Original post by HiggsBoson
Can someone please help me with this question?
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Reply 2
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HiggsBoson
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DSC_0076-compressed.JPG.jpeg
I think this might work.
Reply 3
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Notnek
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Original post by HiggsBoson
DSC_0076-compressed.JPG.jpeg
I think this might work.

Which part do you need help with? Also, please post what you've tried.
Reply 4
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HiggsBoson
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I have done part a and got:
A2=5-4k,
A3=5-5k-4k^2,
I know these are right as my teacher has marked them correct.
Im not sure how to work out the answers using sigma notation though.
Reply 5
Avatar for Notnek
Notnek
21
Original post by HiggsBoson
I have done part a and got:
A2=5-4k,
A3=5-5k-4k^2,
I know these are right as my teacher has marked them correct.
Im not sure how to work out the answers using sigma notation though.

Do you mean you can't do b) and c)?
Reply 6
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HiggsBoson
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Original post by Notnek
Do you mean you can't do b) and c)?


Yeah
Reply 7
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Notnek
21
Original post by HiggsBoson
Yeah

So for b) if you plug r = 1 into the exression inside the sigma you get

1+a11+a_1

then plug r = 2

1+a21+a_2

and r = 3

1+a31+a_3

So ∑r=131+ar=1+a1+1+a2+1+a3\displaystyle \sum_{r=1}^3 1+a_r = 1 + a_1 + 1 + a_2 + 1 + a_3

Can you work this out using your answers to a)? Please post your working if you get stuck.
Reply 8
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HiggsBoson
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Original post by Notnek
So for b) if you plug r = 1 into the exression inside the sigma you get

1+a11+a_1

then plug r = 2

1+a21+a_2

and r = 3

1+a31+a_3

So ∑r=131+ar=1+a1+1+a2+1+a3\displaystyle \sum_{r=1}^3 1+a_r = 1 + a_1 + 1 + a_2 + 1 + a_3

Can you work this out using your answers to a)? Please post your working if you get stuck.

I got 17-9K-4K^2, is this correct?
Reply 9
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Notnek
21
Original post by HiggsBoson
I got 17-9K-4K^2, is this correct?

The numbers are correct but the signs are wrong. Please post your working.
Original post by Notnek
The numbers are correct but the signs are wrong. Please post your working.


(1+4)+(1+5-4k)+(1+5-5K-4k^2)
I added up all the like terms.
Reply 11
Avatar for Notnek
Notnek
21
Original post by HiggsBoson
I have done part a and got:
A2=5-4k,
A3=5-5k-4k^2,
I know these are right as my teacher has marked them correct.
Im not sure how to work out the answers using sigma notation though.

I just noticed that your A3 is incorrect.

It should be 5−k(5−4k)5 - k(5-4k) which becomes

5−5k+4k25 - 5k + 4k^2
Original post by Notnek
I just noticed that your A3 is incorrect.

It should be 5−k(5−4k)5 - k(5-4k) which becomes

5−5k+4k25 - 5k + 4k^2


So the correct answer should be 17-9k+4k^2?
Reply 13
Avatar for Notnek
Notnek
21
Original post by HiggsBoson
So the correct answer should be 17-9k+4k^2?

Yes that's right.
Original post by Notnek
Yes that's right.


Thank you,
Can you please help me with part c please?
Reply 15
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Notnek
21
Original post by HiggsBoson
Thank you,
Can you please help me with part c please?

Try plugging in r = 1 then r = 2 etc. like I showed you in part b). Do this a few times and you should notice a pattern. Post your working if you're unsure.
Original post by Notnek
Try plugging in r = 1 then r = 2 etc. like I showed you in part b). Do this a few times and you should notice a pattern. Post your working if you're unsure.


Sorry I don't understand, isn't it the sum of the first 100 terms.
Reply 17
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Notnek
21
Original post by HiggsBoson
Sorry I don't understand, isn't it the sum of the first 100 terms.

Yes it is but there's a trick to doing this - you don't have to find all 100 terms. Try finding the first few and see what you get. Post your working if you get stuck.
Original post by Notnek
Yes it is but there's a trick to doing this - you don't have to find all 100 terms. Try finding the first few and see what you get. Post your working if you get stuck.

I'm starting to notice a pattern:
a1=4
a2=5-4k
a3=5-5k+4k^2
a4=5-5k-5k^2-4k^3
a5=5-5k-5k^2-5k^3-4k^4.
Im not sure what to do next though
Reply 19
Avatar for Notnek
Notnek
21
Original post by HiggsBoson
I'm starting to notice a pattern:
a1=4
a2=5-4k
a3=5-5k+4k^2
a4=5-5k-5k^2-4k^3
a5=5-5k-5k^2-5k^3-4k^4.
Im not sure what to do next though

For c) you need to consider the expression inside the sigma so for r = 1:

a1+1+ka1=a2+ka1=5−4k+k(4)=5a_{1+1} + ka_1 = a_2 + ka_1 = 5-4k + k(4) = 5

Try doing it for r = 2 and r = 3.

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