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 this

(edited 11 months ago)

Reply 1

Marvel_fan

17

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

pinkrocket

12

I've done this question before and yes it is 6. I think your method is the way you do it

(edited 11 months ago)

Reply 3

_Hello_There_

5

[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

Alevelhelp.1

OP

15

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

pinkrocket

12

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

Marvel_fan

17

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 11 months ago)

Reply 7

Alevelhelp.1

OP

15

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