In Exercises 47-52, use inductive reasoning to predict the next line in each sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct. 1 + 3 = 2 × 2 1 + 3 + 5 = 3 × 3 1 + 3 + 5 + 7 = 4 × 4 1 + 3 + 5 + 7 + 9 = 5 × 5
In Exercises 47-52, use inductive reasoning to predict the next line in each sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct. 1 + 3 = 2 × 2 1 + 3 + 5 = 3 × 3 1 + 3 + 5 + 7 = 4 × 4 1 + 3 + 5 + 7 + 9 = 5 × 5
Solution Summary: The author explains inductive reasoning to predict the next line in the given sequence of computations and then use a calculator to determine whether your conjecture is correct.
In Exercises 47-52, use inductive reasoning to predict the next line in each sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct.
Choose which reasoning process is shown in the following example. Explain your answer.
It can be shown that
1+2+3+...+n=n(n+1)/2.
This formula can be used to conclude that the sum of the first 2000 numbers,
1+2+3+...+2000, is the following.
2000(2000+1)/2=2000(2001)/2=1000(2001),
or 2,001,000
Choose the correct answer below.
A.This is inductive reasoning because it is an educated guess to say that the formula can be used to calculate the sum of the first 2000 numbers.
B.This is deductive reasoning because a specific conclusion is being proved from a general statement.
C.This is inductive reasoning because a specific conclusion is being proved from a general statement.
D.This is deductive reasoning because it is an educated guess to say that the formula can be used to calculate the sum of the first 2000 numbers.
Use the formula for the sum of the first n integers to evaluate the sum given below, then write it in closed form. (For each answer, enter a mathematical expression.)
(a)
6 + 7 + 8 + 9 + ⋯ + 600
(b)
6 + 7 + 8 + 9 + ⋯ + k
Use deductive reasoning to show that the following procedure
produces a number that is three times the original number.
Procedure: Pick a number. Multiply the number by 6, add 10 to the
product, divide the sum by 2, and subtract by 5.
Hint: Let n represent the original number.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Grade 12 and UG/ Introduction to logical statements and truth tables; Author: Dr Trefor Bazett;https://www.youtube.com/watch?v=q2eyZZK-OIk;License: Standard YouTube License, CC-BY