Question

Becky is offered the two deals below. Deal 1: She will get a quarter on the first day of the week. Each day thereafter for one week, she will receive double what she received on the previous day. Deal 2: She will get $4 each day for 1 week. Which statement is true in every aspect regarding these two deals

Answer 1

She should go with deal 1 is greater than by $3.75.

Step-by-step explanation:

The computation is shown below:

As in the first deal we have shown in a geometric sequence

We can represent Deal 1 as a geometric sequence:

`g_n=0.25(2)^(n-1)`

where,

The 0.25 = first term,

2 = common ratio (as it doubles every day)

and n = the term number.

Now for determining the total money amount, first we have to calculate the sum

i.e

`\Sigma_(n=1)^7(0.25)(2)^(n-1)`

After solving this,

we get 31.75.

Now for Deal 2

It could be shown as

4(7) = 28.

So as we can see that the deal 1 is greater than Deal 2