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# c12 geometric sequences help

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1. can someone pls explain part e).. (its only based on part c) forget the rest)
when we are writing the equation why do we put 1.5(1.05)^n-1 > 40 as done in the markscheme not 1.5(1.05)^n > 40 ??? n is the number of days and it is asking for the day so we cant subtract one from the day
i mean day 1 gives n=1 , day 2 n=2 and so on...
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2. (Original post by pondsteps)
can someone pls explain part e).. (its only based on part c) forget the rest)
when we are writing the equation why do we put 1.5(1.05)^n-1 > 40 as done in the markscheme not 1.5(1.05)^n > 40 ??? n is the number of days and it is asking for the day so we cant subtract one from the day
i mean day 1 gives n=1 , day 2 n=2 and so on...
What's the formula for a geometric sequence? Check it in your formula booklet.
3. (Original post by Zacken)
What's the formula for a geometric sequence? Check it in your formula booklet.
yeah ik the formula lol.. i'm saying why are we applying here it does not make sense .. its not giving the number of days, but number of days -1
4. (Original post by pondsteps)
yeah ik the formula lol.. i'm saying why are we applying here it does not make sense .. its not giving the number of days, but number of days -1
The nth term is the nth day.

The geometric sequence gives you as the nth term.

So the nth day is .
5. (Original post by Zacken)
The nth term is the nth day.

The geometric sequence gives you as the nth term.

So the nth day is .
day one so n=1 , 1.5
day 2 so n=2 , 1.5(1.05)
day 3 n=3 , 1.5(1.05)2
day 4 n=4 1.5(1.05)3

so seee what i meant, the days is 1 more than the power so we should put n not n-1
6. (Original post by pondsteps)
day one so n=1 , 1.5
day 2 so n=2 , 1.5(1.05)
day 3 n=3 , 1.5(1.05)2
day 4 n=4 1.5(1.05)3

so seee what i meant, the days is 1 more than the power so we should put n not n-1
Do you understand why it is necessary to use logs on this question?

Try taking logs of both sides of your nth term equation, you'll see...
7. (Original post by pondsteps)
day one so n=1 , 1.5
day 2 so n=2 , 1.5(1.05)
day 3 n=3 , 1.5(1.05)2
day 4 n=4 1.5(1.05)3

so seee what i meant, the days is 1 more than the power so we should put n not n-1
Uhm..

You've just said that day 4 (n=4) means 1.5(1.05)^(3) = 1.5(1.05)^(4-1)

So day n (n=n) means 1.5(1.05)^(n-1)
8. (Original post by Zacken)
Uhm..

You've just said that day 4 (n=4)means 1.5(1.05)^(3)= 1.5(1.05)^(4-1)

So day n (n=n) means 1.5(1.05)^(n-1)
exactly soo when in the final answer we find the day it is the number of days -1 ??
9. (Original post by pondsteps)
exactly soo when in the final answer we find the day it is the number of days -1 ??
Yes? That's what they've done. n-1 > 67.something so n > 68.something so n = 69
10. (Original post by Zacken)
Yes? That's what they've done. n-1 > 67.something so n > 68.something so n = 69
This is probably something you could answer.

Generally, is the following situation true?

Whenever the geometric progression is increasing we can use a > sign, and when the GP is decreasing, we will use a < sign?

For instance, in this question, the GP is increasing each time, so this is why a > sign is used yes?

Consider a depreciating car, with a question such as 'Find the year when the car value falls below £1000' in this case we would use a < sign?
11. (Original post by PedanticStudent)
This is probably something you could answer.

Generally, is the following situation true?

Whenever the geometric progression is increasing we can use a > sign, and when the GP is decreasing, we will use a < sign?

For instance, in this question, the GP is increasing each time, so this is why a > sign is used yes?

Consider a depreciating car, with a question such as 'Find the year when the car value falls below £1000' in this case we would use a < sign?
Well, you'd use a < sign when the word below/less/synonyms are present which just so happens to be associated with decreasing GP's so you're right in that sense, but I'd like to stress that the < sign comes from wanting the quantity to be less than some other quantity (which just so happens to necessitate a decreasing GP).
12. (Original post by Zacken)
Well, you'd use a < sign when the word below/less/synonyms are present which just so happens to be associated with decreasing GP's so you're right in that sense, but I'd like to stress that the < sign comes from wanting the quantity to be less than some other quantity (which just so happens to necessitate a decreasing GP).
Excellent. Thank you!
13. (Original post by Zacken)
Yes? That's what they've done. n-1 > 67.something so n > 68.something so n = 69
should i always just stick to the equation and thats it cos i just dont seem to get it
14. (Original post by pondsteps)
should i always just stick to the equation and thats it cos i just dont seem to get it
Do you understand the n-1 > 67.(something) bit? Which particular bit aren't you getting?
15. (Original post by Zacken)
Do you understand the n-1 > 67.(something) bit? Which particular bit aren't you getting?
no thats the part thats confusing me.. when the day was three the power was 2, so we should add one to what we get in order to get the day !! bcz what we got is the power not the days they are different
16. (Original post by pondsteps)
no thats the part thats confusing me.. when the day was three the power was 2, so we should add one to what we get in order to get the day !! bcz what we got is the power not the days they are different
Hmm, okay - do you understand 1.5(1.05)^(n-1) > 40.

Once you understand that then you just need to solve that inequality and ignore anything about context or whatever, you need to think a bit to write that inequality down and then you can stop thinking and just solve it on autopilot.
17. (Original post by Zacken)
Hmm, okay - do you understand 1.5(1.05)^(n-1) > 40.

Once you understand that then you just need to solve that inequality and ignore anything about context or whatever, you need to think a bit to write that inequality down and then you can stop thinking and just solve it on autopilot.
lol i just thought of it and realized i was confusing myself thanks a lot for helping!
18. (Original post by pondsteps)
lol i just thought of it and realized i was confusing myself thanks a lot for helping!

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