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
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
1 answer
1 answer