The small squares on a chessboard can be combined to form larger squares. For example, there are sixty-four 1x1 squares and one 8x8 square. Use inductive reasoning to determine how many 2x2 squares, 3x3 squares, and so on, are on a chessboard. What is the total number of squares on a chessboard?

204

Step-by-step explanation:

Given that a 1x1 square can be located in 8 places horizontally and 8 places vertically,

Then we have 1x1 squares: 8² = 64

Again the subsequent squares will be written as

2x2 squares: 7² (2 squares in 7 places both horizontal and verticals) = 49

3x3 squares: 6² (3 squares in 6 places both horizontal and verticals)= 36

4x4 squares: 5² (4 squares in 5 places both horizontal and verticals)= 25

5x5 squares: 4² (5 squares in 4 places both horizontal and verticals)= 16

6x6 squares: 3² (6 squares in 3 places both horizontal and verticals)= 9

7x7 squares: 2² (7 squares in 2 places both horizontal and verticals)= 4

8x8 squares: 1² (8 squares in 1 places both horizontal and verticals)= 1

Hence, the total number of squares on chessboard is 1+4+9+16+25+36+49+64 = 204.

204

Step-by-step explanation:

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5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116