Asked by keneth
1.what is the least number of terms of the GP.2,4, 8.....that will give a sum greater than 1500000 2.Aball allowed to drop from heigth of 3m on to a horizontal ground rebounds to3/4 of its previous heigth.Find to the nearest metre,the total distance the ball will have traveled when it hits the ground for the eight time
Answers
Answered by
Reiny
1.
In your GP, a = 2, r = 2
sum(n) < 1500000
a(r^n - 1)/(r-1) > 1500000
2(2^n - 1)/(2-1) > 1500000
2^n - 1 > 750000
2^n > 750001
take log of both sides , and use log rules
n log2 > log 750001
n > log 750001/log2
n > 19.5
at n = 19 we won't be there, so we need 20 terms
check: sum(20) = 2(2^20 - 1)(1) = 2097150
sum(19) = 2(2^19 - 1)/1 = 1048574 which is < 1500000
2. make a sketch of the first few bounces.
Notice that the first bounce is only a one-way down, but the second , third, fourth, etc, have an up and a down and they are a GP
good luck
In your GP, a = 2, r = 2
sum(n) < 1500000
a(r^n - 1)/(r-1) > 1500000
2(2^n - 1)/(2-1) > 1500000
2^n - 1 > 750000
2^n > 750001
take log of both sides , and use log rules
n log2 > log 750001
n > log 750001/log2
n > 19.5
at n = 19 we won't be there, so we need 20 terms
check: sum(20) = 2(2^20 - 1)(1) = 2097150
sum(19) = 2(2^19 - 1)/1 = 1048574 which is < 1500000
2. make a sketch of the first few bounces.
Notice that the first bounce is only a one-way down, but the second , third, fourth, etc, have an up and a down and they are a GP
good luck
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