A worker is paid

0.07 on the first day,
0.14 on the second day,
$0.28 on the third day, and so on.
How much is the worker paid in total after working for 26 days?

Select one:
a. Between 0 and 1000(FALSE)
b. Between 1000and2 000 000
c. Between 2000000and4 000 000 (FALSE)
d. Over $4 000 000

A sequence of numbers each of which is progressively increased by the same factor, in this case, the factor is 7, is known as a geometric time 7 x 26

In your problem, n = 26 (the number of days), so, the total number of
money received for 26-days work would be: A

Sum of a geometric series = a(r^n - 1)/(r - 1)

here a=.07 , r=2 , n = 26

sum = .07(2^26 - 1)/(2-1)
= $4,697,620.41

In this case, the factor is 2, not 7.

So, with a starting value of a = 0.07,
S26 = .07(2^26-1)/(2-1) = 4,697,620.41 or (D)
(C) is correct for the amount paid on the 26th day, not the total

To calculate the total amount the worker is paid after working for 26 days, we need to determine the pattern and then sum it up.

From the given information, we can see that the worker's pay doubles each day.

So, on the first day, the worker is paid 0.07.
On the second day, the worker is paid 2 * 0.07 = 0.14 (double the amount from the previous day).
On the third day, the worker is paid 2 * 0.14 = 0.28 (double the amount from the previous day).

This pattern continues, so we can calculate the worker's pay for each day using the formula: pay = 0.07 * 2^(n-1), where n is the day number.

Let's calculate the worker's pay for each day:

Day 1: pay = 0.07 * 2^(1-1) = 0.07 * 2^0 = 0.07
Day 2: pay = 0.07 * 2^(2-1) = 0.07 * 2^1 = 0.14
Day 3: pay = 0.07 * 2^(3-1) = 0.07 * 2^2 = 0.28
Day 4: pay = 0.07 * 2^(4-1) = 0.07 * 2^3 = 0.56
.
.
.
Day 26: pay = 0.07 * 2^(26-1) = 0.07 * 2^25 = 293,601.28

Now, to find the total pay after 26 days, we need to sum up the pay for each day:

Total pay = pay(day1) + pay(day2) + pay(day3) + ... + pay(day26)

Using the formula for the sum of a geometric progression, which is given by: S = a * (1 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms in the sequence.

Total pay = 0.07 * (1 - 2^26) / (1 - 2) = 0.07 * (1 - 67,108,864) / (-1) = 0.07 * (67,108,863) = $4,694,620.41

Therefore, the worker is paid over $4,000,000 after working for 26 days. So the answer is option d. Over $4,000,000.