To find: the number of bricks in the patio.
Answer to Problem 75E
The total numbers of the bricks in the patio are, 405.
Explanation of Solution
Given information:
A brick patio has the approximate shape of a trapezoid, as shown in the figure. The patio has 18 rows of bricks. The first row has 14 bricks and the 18th row has 31 bricks.
Given figure
Concept used:
An arithmetic sequence of n terms, has the form
That is
Common difference can be defined by d .
nth term of the arithmetic sequence has the form
Where
Sum of an arithmetic finite sequence has the form
Here, n is number of terms,
Calculation:
Let us consider the following figure
The bricks are arranged in the arithmetic sequence in the subsequent rows, that is, the difference between the consecutive rows is constant.
Therefore, the total number of bricks can be found out by calculating the partial sum of this arithmetic series up to 189 terms.
We are given that,
Substituting in the formula, we get
Therefore, the total numbers of the bricks in the patio are, 405.
Chapter 8 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning