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...