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Post your AS-Level Mathematics (P1 and M1) doubts here.

Hadi Murtaza

Hadi Murtaza

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Snowysangel said:
When is a progression convergent and even is it divergent? In p1
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Convergent is when succesive values of a sequence get closer n closer to a certain number and this is when 0 < r < 1 . For example da sequnce 16/n² approches 0 as n increases.
Divergent is when succesive values of a sequence get farther apart each time n increases and this is when r > 1. for example da sequence n² keeps on increasing and increasing.
 
S

Snowysangel

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Can someone please solve this, step by step:
In a geometric progression, the second term is 9 less than the first term. The sum of the second and third terms is 30. Given that all the terms of the progression are positive, find the first term.
 
Jelleh Belleh

Jelleh Belleh

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Snowysangel said:
Can someone please solve this, step by step:
In a geometric progression, the second term is 9 less than the first term. The sum of the second and third terms is 30. Given that all the terms of the progression are positive, find the first term.
Click to expand...

Given: a2 = a - 9
an = a x r^(n-1)
=> a - 9 = ar
= a - ar = 9
=> a(1-r) = 9
Given: a2 + a3 = 30
a2 = ar
a3 = ar^2
=> ar + ar^2 = 30
=> ar(1+r) = 30

Divide the 2 eqns:
ar(1+r)/a(1-r) = 30/9
the a cancels out
=> you end up with: 3r^2 + 13r -10 = 0
Solve for r: r=2/3 or r=-5
Substitute the 2 values of r in the equation: a(1-r)=9 to find a, and then use the value of a to find a2
The value of a that gives a +ve value of a2 is the correct answer
==> a=27
 
Rockstar RK

Rockstar RK

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Snowysangel

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Jelleh Belleh said:
Given: a2 = a - 9
an = a x r^(n-1)
=> a - 9 = ar
= a - ar = 9
=> a(1-r) = 9
Given: a2 + a3 = 30
a2 = ar
a3 = ar^2
=> ar + ar^2 = 30
=> ar(1+r) = 30

Divide the 2 eqns:
ar(1+r)/a(1-r) = 30/9
the a cancels out
=> you end up with: 3r^2 + 13r -10 = 0
Solve for r: r=2/3 or r=-5
Substitute the 2 values of r in the equation: a(1-r)=9 to find a, and then use the value of a to find a2
The value of a that gives a +ve value of a2 is the correct answer
==> a=27
Click to expand...
But you can't always divide to elimate a variable right? So how can you solve the two equations using substation, and why can't we subtract to eliminate I e of the variables ? :S
 
Jelleh Belleh

Jelleh Belleh

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Snowysangel said:
But you can't always divide to elimate a variable right? So how can you solve the two equations using substation, and why can't we subtract to eliminate I e of the variables ? :S
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I've been able to solve every question similar to this I came across using this method. There might be another way of solving these types of questions, but i'm not aware of it, sorry. If you find a question where this method doesn't work, do post it. :)
 
Jelleh Belleh

Jelleh Belleh

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Jelleh Belleh

Jelleh Belleh

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Snowysangel said:
But how do you solve it by dividing the equations? :S and why can't solve the equation I originally wrote through simple elimination?
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Why would you want to divide them when you can easily use elimination?
You can go ahead and try using elimination on the first question. I for one, was unable to solve using this method. There might be a different way of solving it besides dividing the 2 equations but, like I said, I don't know it. Sorry.
 
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