The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

c2 geometric sequences question

cant seem to answer this question:

in a geometric progression, the second term is -4 and the sum to infinity is 9, find the common ratio?

i can see that a= -4/r and sum to infinity = a/1-r

the answer is -1/3 (teacher gave us the answers) but i cant get to that. any help would be appreciated
Reply 1
Avatar for Swayum
Swayum
18
a = -4/r is correct

You also know the sum to infinity formula is a/1-r and you're told in the question that this equals 9

So you know a/(1-r) = 9

You have two equations and two unknowns, so what do you do?
Reply 2
Avatar for nuodai
nuodai
17
What answer do you get? You have enough information to do the question; substitute a=−4ra=-\frac{4}{r} into 9=a1−r9=\frac{a}{1-r} and solve for rr (it's probably easiest to multiply through by 1−r1-r first).
Reply 3
Avatar for xHuStLeR23
xHuStLeR23
1
How do you know r= -1/3 as opposed to 4/3?
Reply 4
Avatar for nuodai
nuodai
17
Original post by xHuStLeR23
How do you know r= -1/3 as opposed to 4/3?


Because we need −1<r<1-1 < r < 1 for the sum to infinity to converge.
Reply 5
Avatar for matt730
matt730
OP
Thanks for the help guys, had a bit of a blank and couldnt see that it was a quadratic giving r=4/3 and r=-1/3. i have no idea why it cant be 4/3, maybe my teacher made a mistake
Reply 6
Avatar for nuodai
nuodai
17
Original post by matt730
i have no idea why it cant be 4/3


Work out the 10th, 100th and 1000th terms when it's -1/3, and again when it's 4/3, and you'll see why.
Reply 7
Avatar for matt730
matt730
OP
Work out the 10th, 100th and 1000th terms when it's -1/3, and again when it's 4/3, and you'll see why.

ahhh now it makes sense. Its been a long day of c2 revision lol

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you