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Help urgent maths sequence and series

Help I don’t get how to do this question I know the sum to infinity formula
It’s in my forums booklet
A/1-r
But idk how to do thisIMG_2653.jpeg
(edited 12 months ago)
Reply 1
Is the answer actually 6? because would multiplying each term mean the new sequence's first term is -2a (if a is the first term of the original sequence) and the common ratio is still the same as before. That would mean the new sum is -2a/(1-r) = -2(-3) which is 6.

But I'm not 100% sure of this method
Reply 2
I've done this question before and yes it is 6. I think your method is the way you do it
(edited 12 months ago)
[sum to infinity] = [term 1] + [term 2] + [term 3] + [term 4] + ...
if you multiply each term by -2 then you get [new sum to infinity] = (-2) * [term 1] + (-2) * [term 2] + (-2) * [term 3] + (-2) * [term 4] + ...
therefore [new sum to infinity] = (-2) * ( [term 1] + [term 2] + [term 3] + [term 4] + ... ) = (-2) * [old sum to infinity]
so as the [old sum to infinity] = -3
[new sum to infinity] = (-2) * (-3) = 6
Reply 4
Original post by Marvel_fan
Is the answer actually 6? because would multiplying each term mean the new sequence's first term is -2a (if a is the first term of the original sequence) and the common ratio is still the same as before. That would mean the new sum is -2a/(1-r) = -2(-3) which is 6.

But I'm not 100% sure of this method


Yea the answer is 6 but idk how 😭 have u got your maths a level this year??
Reply 5
I don't know if my method is the best but I just thought that if every term had been multiplied by -2, then the sum to infinity would be times by -2 aswell, which means the answer would be 6. This is the same as what @_Hello_There_ has written i've just realised
Reply 6
Original post by Alevelhelp.1
Yea the answer is 6 but idk how 😭 have u got your maths a level this year??


Yeah I have! have you as well?

First sequence: a + ar + ar^2 + ar^3 + ...
Second sequence: -2a + -2ar + -2ar^2 + -2ar^3 + ... = -2a + (-2a)r + -(2a)r^2 + (-2a)r^3 + ...

Not sure if that helps at all but its how I visualize it
(edited 12 months ago)
Reply 7
Original post by Marvel_fan
Yeah I have! have you as well?

First sequence: a + ar + ar^2 + ar^3 + ...
Second sequence: -2a + -2ar + -2ar^2 + -2ar^3 + ... = -2a + (-2a)r + -(2a)r^2 + (-2a)r^3 + ...

Not sure if that helps at all but its how I visualize it


Yesss mine is on Tuesday my pure test I’m doing aqa btw wbu I’m so scared I’m gonna flop… I’ve been getting LOW Cs 😭😭😭
plz pray for me 🤲
(edited 12 months ago)
Reply 8
Original post by Alevelhelp.1
Yesss mine is on Tuesday my pure test I’m doing aqa btw wbu I’m so scared I’m gonna flop… I’ve been getting LOW Cs 😭😭😭
plz pray for me 🤲


No you've got this!! I do edexcel but have further on monday too. Just keep doing your practice questions and I'm sure you'll do great :smile:
Original sum = -3.

New sum = -2 * Original sum = -2 * -3 = 6.

One does not need to deal with the series terms at all in this case.

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