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# Geometric sequences - C2 help?

1. I've got a few problems with geometric sequences and I'd be grateful for some help

1. A competitor in a pie-eating contest eats one-third of his pie in the first minute. In each subsequent minute he eats three-quarters of the amount he ate in the previous minute. Find an expression for the amount of pie he has left to eat after n minutes. Show that he takes between 4 and 5 minutes to finish the pie.

I'm unsure how to do the first part, but I just wrote out the sequence...

u1 = 1/3. u2 = 1/4. u3 = 3/16. u4 = 9/64.

For the second part, I did 1< 0.5(1-0.75^n)
2<1-0.75^n => 1<-0.75^n

Was going to log both sides, but then you can't log both sides...

2. A 'supa-ball' is thrown upwards from ground level. It hits the ground after 2 seconds and continues to bounce. The time it is in the air for a particular bound is always 0.8 of the time for the previous bounce.

Well I think the sequence goes like, 2, 1.6, 1.28...

I thought it would be like Un = ar^n-1

0 = 2*0.8^n-1.

If you work that out, then you get n = 0... :/

Thanks for any help given
2. In 1 what formula are you using

did you mean 1/3 where you have 0.5
3. (Original post by TenOfThem)
In 1 what formula are you using

did you mean 1/3 where you have 0.5
Erm isn't it 1/3 as it says he eats 1/3 of the pie in the first minute?

I was using the Sn = (a(1-r^n))/1-r formula - sum of geometric sequences. Is that wrong?
4. a=1/3 r=3/4 sn=1

You want to find out when the whole pie has been eaten, which is when the sum of the geometric series is equal to one.
5. (Original post by MedicalMayhem)
Erm isn't it 1/3 as it says he eats 1/3 of the pie in the first minute?

I was using the Sn = (a(1-r^n))/1-r formula - sum of geometric sequences. Is that wrong?
I am still wondering where the 0.5 came from
6. (Original post by VictorDeLost)
a=1/3 r=3/4 sn=1

You want to find out when the whole pie has been eaten, which is when the sum of the geometric series is equal to one.
Hm even if it is equal to 1, won't you have 1=-0.75^n? I'm a bit unsure, but if you multiply both sides by -1, it won't become -1=0.75^n will it?

(Original post by TenOfThem)
I am still wondering where the 0.5 came from
Erm as it's a(1-r^n) / 1-r. 1-r = 2/3 and a = 1/3. So (1/3)/ 2/3 = 1/2.
7. Why do you have 1-3/4 = 2/3
8. (Original post by TenOfThem)
Why do you have 1-3/4 = 2/3
Ah yes, such a silly mistake :/

So you're left with -0.25 = -0.75^n.

I recall something my teacher saying about you not being about to multiply or something to bases. Does it mean that I can't multiply both sides by -1?

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