In order to save one million naira for the purchase of some goods a man save #1,#2,#4 #8 on the first,second,third and fourth day respectively.At this rate assuming that no interest was added

Question

(a):what amount was saved on the 15th day?
(b):at least how many days were needed to accumulate the one million naira?....plz help

Answer 1

first day -- 1 = 2^0
2nd day -- 2 = 2^1
3rd day -- 4 = 2^2
..
15th day ---- 2^14 or 16384

accumulate means you want the sum to be 1 million
we have a geometric series with
a = 1
r = 2
n = ??
sum(n) = 1000000

sum(n) = a(r^n - 1)/(r-1)
1000000 = 1(2^n - 1)/1
2^n = 1000001
take log of both sides and use log rules
n log2 = log 1000001
n = 19.93

so 19 days are not enough, so it must be 20 days