Answer:
32,767 pennies
Explanation:
The number of pennies saved by Joe for the first four days forms the sequence below:
[tex]1,2,4,8\cdots[/tex]
We want to determine the total size of Joe's collection on the 15th day.
The sequence above forms a geometric sequence in which:
• The first term, a1 = 1
,
• The common ratio, r = 2/1=4/2=2
The sum of a geometric sequence is determined using the formula:
[tex]S_n=\frac{a_1(r^n-1)}{r-1},r>1[/tex]
On the 15th day: n=15
[tex]\begin{gathered} S_{15}=\frac{1(2^{15}-1)}{2-1} \\ =2^{15}-1 \\ =32768-1 \\ =32767 \end{gathered}[/tex]
If Joe continues with this pattern, he will have 32,767 pennies on the 15th day.
