Question

I need help with this asap PLEASE CHECK WORK WHEN FINISHED question 8

Answer 1

32,767 pennies

Explanation:

The number of pennies saved by Joe for the first four days forms the sequence below:

`1,2,4,8\cdots`

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:

`S_n=(a_1(r^n-1))/(r-1),r>1`

On the 15th day: n=15

`\begin{gathered} S_(15)=(1(2^(15)-1))/(2-1) \\ =2^(15)-1 \\ =32768-1 \\ =32767 \end{gathered}`

If Joe continues with this pattern, he will have 32,767 pennies on the 15th day.