Concept explainers
(a)
Find the number of squares there are in the third figure
(a)
Answer to Problem 32PPS
In the 3rd figure the number of square is 14
Explanation of Solution
Given:
There is a total 5 squares in the second figure. How many squares are there in the third figure?
Concept Used:
1st figure is having one square
2nd figure is having 5 squares
3rd figure should be 14 squares.
Thus, in the 3rd figure the number of square is 14
(b)
Write a sequence for the first five figures.
(b)
Answer to Problem 32PPS
The sequence for the first five figures: 1, 5, 14, 30, 55
Explanation of Solution
Given:
Write a sequence for the first five figures.
Concept Used:
1st figure is having one square
2nd figure is having 5 squares
3rd figure should be 15 squares.
4th figure should be 30 squares.
5th figure should be 55 squares.
The sequence for the first five figures: 1, 5, 14, 30, 55
Thus, The sequence for the first five figures: 1, 5, 14, 30, 55
(c)
Find the number of squares in the 8 x 8 checker board.
(c)
Answer to Problem 32PPS
The number of squares in a 8 x 8 checker board is 204.
Explanation of Solution
Given:
How many squares are there in a standard 8 x 8 checker board?
Concept Used:
The recursive formula for the sequence:
Calculation:
The recursive formula for the sequence:
Substitute n = 8; the number of squares in 8 x 8 checker board is
Thus, the number of squares in a 8 x 8 checker board is 204.
(d)
Write a formula to represent the number of squares in an n x n grid.
(d)
Answer to Problem 32PPS
Formula to represent the number of squares in n x n grid is
Explanation of Solution
Given:
Write a formula to represent the number of squares in an n x n grid.
Concept Used:
Formula to represent the number of squares in n x n grid is
Thus, Formula to represent the number of squares in n x n grid is
Chapter 10 Solutions
Glencoe Algebra 2 Student Edition C2014
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