There are 8 rows and 8 columns, or 64 squares
on a chessboard. Suppose you place 1 penny on
Row 1 Column A, 2 pennies on Row 1 Column
B, 4 pennies on Row 1 Column C, and so on ...
How many pennies in Row 1?
How many pennies in Row 1-4?
How many pennies on the entire chessboard?

255

4,294,967,295

18,446,744,073,709,551,615

Step-by-step explanation:

Geometric Sequence

Each term of a geometric sequence is obtained by multiplying (or dividing) the previous term by a constant number called common ratio (r). The recursive formula for each term n is

And the general formula is

for n>=1

We place 1 penny on the first cell (square) (row 1, column A). That is the value of a1=1. Now each new cell will have double pennies as much the previous cell. The common ratio is r=2. Thus, the following general formula gives us the number of pennies on the cell n

This gives us the sequence 1,2,4,8,16,32,...,

To get the sum of n terms, we notice the sum forms the sequence 1, 3, 7, 15, 31, 63,... which we can transform as

2-1, 4-1, 8-1, 16-1, 32-1, 64-1,...

Or equivalently

The formula for the sum of n terms is, then

Now we are ready to answer the questions

How many pennies in Row 1?

Row 1 has n=8 cells, thus

How many pennies in Row 1-4?

The first 4 rows contain 4*8=32 cells, thus

How many pennies on the entire chessboard?

Here n=64

For a 0.25 pfor b o.3pp (0.25+0.3)=0.28

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )