Aking 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 18? 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.)

Part 1) On square 18 should be place

Part 2) The total number of grains of wheat is

Part 3) The total weight is

Step-by-step explanation:

we know that

In a Geometric Sequence each term is found by multiplying the previous term by a constant

Part A) How many grains of wheat should be placed on square 18?

In this problem we have

a1=1

a2=2

a3=4

a4=8

The common ratio (r) is equal to

a2/a1=2/1=2

a3/a2=4/2=2

a4/a3=8/4=2

so

r=2

the explicit rule for the nth term is equal to

For n=18

we have

a1=1

r=2

substitute

Part 2) Find the total number of grains of wheat on the board

we know that

The formula of the sum in a geometric sequence is equal to

we have

a1=1

r=2

n=64

substitute

Part 3) Find the total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pound.)

To obtain the total weight multiply the total grains by (1/7,000)

Round to the nearest pound

10 cm

step-by-step explanation:

if the polygon is a rectangle, then the perimeter is x+x+y+y. using the values that you gave, the perimeter is 3+3+2+2=10cm.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.