A worker is paid $0.10 on the first day, $0.30 on the second day, $0.90 on the third day, $2.70 on the fourth day, and so on.
Notice that the pattern of getting wages is 3 times of the previous day.
Like the wages for the first day= 0.10
Second day = 0.10*3 = 0.30
Third day = 0.30 *3 = 0.90 And so on.
Hence the wages represent a geometric sequence where
first term: a = 0.10 and common ratio: r = 3.
And we need to find the total does the worker earn after working 14 days:[tex] S_{14} [/tex].
Formula to find the sum of nth term a geometric sequence is:
[tex] S_{n} =\frac{a(r^n-1)}{r-1} [/tex]
=[tex] \frac{0.10(3^{14}-1)}{3-1} [/tex]
=[tex] \frac{0.10(4782969-1)}{2} [/tex]
=[tex] \frac{0.10(4782968)}{2} [/tex]
=[tex] \frac{478296.8}{2} [/tex]
= 239148.4
So, he will earn $239148.40 fter 14 days.
Hope this helps you.
