A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of​ wheat, on the third​ square, four grains of​ wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining​ squares, how many grains of wheat should be placed on square 24 ​? Also find the total number of grains of wheat on the board at this time and their total weight in pounds.​ (Assume that each grain of wheat weighs​ 1/7000 pound.)

Answer:

1) 8,388,608 grains of wheat.

2) 16,777,215 grains of wheat.

3) 239,674.5 pounds.

Step-by-step explanation:

Question 1)

We know that on the first square, there is 1 grain of wheat.

On the second, 2 grains of wheat.

On the third, 4 grains of wheat.

And on the fourth, 8 grains of wheat.

Therefore, we have a geometrically increasing sequence. It looks like:

1, 2, 4, 8...

Therefore, to find the number of grains on the 24th square, we can write an explicit formula.

The standard form for the explicit formula for a geometric sequence is:

[tex]x_n=a(r)^{n-1}[/tex]

Where a is the initial amount, r is the common ratio, and n is the nth term (starting from 1).

We know that the initial term a is 1 because there’s one grain of wheat on the first square.

And the common ratio will be 2 because each square has double the amount of the previous square.

So, substitute 1 for a and 2 for r. This yields:

[tex]x_n=1(2)^{n-1}\\[/tex]

We can simplify this:

[tex]x_n=2^{n-1}[/tex]

So, to find the amount of wheat on the 24th square, we simply need to substitute 24 for n and evaluate. So:

[tex]x_{24}=2^{24-1}=2^{23}[/tex]

Evaluate. Use a calculator:

[tex]x_{24}=8,388,608[/tex]

Therefore, on the 24th square, there are 8,388,608 grains of wheat.

Question 2.1)

We want to find the total number of grains of wheat on the board at this time.

In other words, we want to find the sum of our geometric sequence when n is 24.

The formula for the sum of a geometric series is:

[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]

Where rⁿ is the value of the number of terms n, r is the common ratio, and a is the initial term.

We want to find the sum after 24 times. So, n is 24.

So, substitute 24 for n, 2 for r, and 1 for a. This yields:

[tex]S_{24}=\frac{(1)(2^{24}-1)}{2-1}[/tex]

Evaluate. Use a calculator:

[tex]S_{24}=16, 777, 215[/tex]

Therefore, the total sum of the number of grains of wheat at the board at the 24th square is 16,777,215.

Question 2.2)

And to find the weight, we will just have to multiply our total amount by 1/7000. So:

[tex]W=16777215(\frac{1}{70})[/tex]

Use a calculator:

[tex]W=239,674.5\text{ lbs}[/tex]

So, the total weight is 239,674.5 pounds.

List and describe the characteristics of a wave

The area, a, of a square whose side length is n

After how many weeks will Donald and Ralph have the same amount of money saved?

A-6wks
B-20wks
C-12wks

Write the equation of the line:
(0,3); slope -2

the nth term of a sequence is 20-n^2
a) find the third term of the sequence
b) which term in the sequence is the first to have a negative value ​

Which travels faster: a car that travels 6 miles in 10 minutes at a constant speed, or a train that travels 6 miles in 8 minutes at a constant speed? Explain how
you

During the 2011-12 NBA season, LeBron James had an average of 30.3 points per game. The mean and standard deviation for the league were 7.65 points per game and 6.64 points per game, respectively. That same season the WNBA was led by Diana Taurasi who averaged 21.6 points per game. The mean and standard deviation for the entire WNBA that year were 8.13 points per game and 4.77 points per game, respectively. Who had the more remarkable performance compared to the rest of their league

Can only polygons be rotated

A cheese maker changes the temperature of her milk at a rate of -2 per minute. What is the change in the temperature of the milk after 25 minutes?


please be sure about your answer !!

Select all of the zeros of the function f(x)=(3x−4)(x+2).




4


2


43


− 43


− 2


− 4

My math teacher,mr.numeric, went to the auto show last weekend. I made the mistake of asking him what he saw.here was his response: I’m glad you asked. I made several interesting observations. As you might have guessed, every red car was a sports car, but I found it odd that half of all the blue cars were sports cars. Interestingly, a salesman told me that half of all the sports cars were red. I counted 40 blue cars and 30 red cars. Now can you tell me how many sports cars were neither blue nor red?

50 BRAINLY POINTS PLS HELP

What is the value of y?
B
60°
12
12
ro
60°
А
12 to 60

Which expression is equivalent to - 3/4 divided (-8/12)

|x |-8= -5
what's the answer​

During the first hour of a snow storm 1 2/8 inches of snow fell in the next hour 4 3/8 inches fell in the third hour the snow stopped and 1 inch of snow melted how much snow was on the ground at the end of the third hour

What is the reciprocal of 4/12?​

Two trains leave a station, one headed due west and the other headed due south. How fast is the southern bound train moving if the west bound train is 15 miles from the station traveling at a constant speed of 35 mph, the distance between the trains is 24 miles, and the distance between them is increasing at a rate of 25 mph.

Brandon is deciding between two truck rental companies. Company A charges an initial fee of $75 for the rental plus $2 per mile driven. Company B charges an initial fee of $35 for the rental plus $3 per mile driven. Let AA represent the amount Company A would charge if Brandon drives xx miles, and let BB represent the amount Company B would charge if Brandon drives xx miles. Write an equation for each situation, in terms of x, and determine which company would be cheaper if Brandon needs to drive 45 miles with the rented truck.

A bakery sells 20 pies, 30 cakes, and 35 muffins on Saturday. The bakery sells
10 pies, 18 cakes, and 28 muffins on Sunday. Which ratio is the smallest?
O A. Number of pies to cakes sold on Saturday
B. Number of cakes to muffins sold on Saturday
C. Number of pies to cakes sold on Sunday
D. Number of cakes to muffins sold on Sunday

Robert earned $300 for 6 hours of work. How much did he make in dollars per hour?
Robert earned $
per hour



Will mark brainliest
Q

What is the multiplicative identity of the complex number –4 + 8i

PLEASE ANSWER IMMEDIATELY!!!

Help I’ll mark you as the brainliest
No answer choice
parallel to y = 5x – 7 but contains (-1,-3)

The monthly cost of running a small business consists of retail space rental at $2400, wages at $1800 and utilities at $480. If the retail space rental and wages are decreased by 5% and 6% respectively, while utilities are increased by 7%, find the percentage increase or decrease in the monthly cost of running the business.

I dont know how I need help on how to do it​

List 5 significant advances in architecture Eastern Indians made

Please help me............

A coin is biased such that a is times as likely to occur as a tail. Find the expected number of when this coin is tossed twice.

Can someone help me answer these please?