Explanation Given: The arithmetic sequences are i. 2 , 4 , 6 , 8 , … , 200 ii. 1 , 3 , 5 , 7 , 9 , … , 199 iii. 5 , 13 , 21 , 29 , … , 157 Approach: (1) The arithmetic mean of the numbers x 1 , x 2 , … , x n is given by x ¯ = x 1 + x 2 + ⋯ + x n n . (2) The middle value of an ordered set of numbers is called median. If the scores has odd number, then the median is middle score and if the score has even number, then the median is the mean of middle two scores. (3) The sum of the arithmetic sequence is S n = n 2 ( a + a n ) , where n is the number of total terms, a is the first term and a n is the last term. Calculation: i. Since the data is in arithmetic sequence with the difference between each term is 4 − 2 = 2 , then the mean of the arithmetic sequence will be S n n . Since the difference between each term is 2 , then the total number of terms will be a n = a + ( n − 1 ) d 200 = 2 + ( n − 1 ) ( 2 ) 200 − 2 2 = n − 1 n = 100 Now, the sum of arithmetic sequence is S n = 100 2 ( 2 + 200 ) = 100 2 ( 202 ) = 10100 So, the mean will be, Mean = S n n = 10100 100 = 101 Also, the median of the arithmetic sequence will be first term + last term 2 . So, the median will be, Median = 2 + 200 2 = 202 2 = 101 ii. Since the data is in arithmetic sequence with the difference between each term is 3 − 1 = 2 , then the mean of the arithmetic sequence will be S n n . Since the difference between each term is 2 , then the total number of terms will be a n = a + ( n − 1 ) d 199 = 1 + ( n − 1 ) ( 2 ) 199 − 1 2 = n − 1 n = 100 Now, the sum of arithmetic sequence is To determine (b) To find: The conjecture about the mean and the median of any arithmetic sequence.

A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)

12th Edition

ISBN: 9780321987297

Author: Rick Billstein, Shlomo Libeskind, Johnny Lott

Publisher: PEARSON

See similar textbooks

Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

Videos

Question

Chapter 10.4B, Problem 12A

To determine

(a)

To find:

The mean and median of the sequences 2,4,6,8,…,200, 1,3,5,7,9,…,199 and 5,13,21,29,…,157.

To determine

(b)

To find:

The conjecture about the mean and the median of any arithmetic sequence.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.4B, Problem 11A

Chapter 10.4B, Problem 13A

Students have asked these similar questions

3) Prove that in extracting real mode ø, from a complex measured mode o, by maximizing the function: maz | ቀÇቃ | ||.|| ||.||2 is equivalent to the solution obtained from the followings: max Real(e)||2

Draw the unit circle and plot the point P=(8,2). Observe there are TWO lines tangent to the circle passing through the point P. Answer the questions below with 3 decimal places of accuracy. L1 (a) The line L₁ is tangent to the unit circle at the point 0.992 (b) The tangent line 4₁ has equation: y= 0.126 x +0.992 (c) The line L₂ is tangent to the unit circle at the point ( (d) The tangent line L₂ has equation: y= 0.380 x + x × x)

Please help me with these questions. I am having a hard time understanding what to do. Thank you

Chapter 10 Solutions

A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)

Ch. 10.1 - Read about basic ideas of statistics in Common...Ch. 10.1 - Suggest how students at different grades might...Ch. 10.1 - Examine grade-school books to see what types of...Ch. 10.1 - Mathematical Connections What are the Nielsen...Ch. 10.1 - Prob. 7MC Ch. 10.1 - National Assessment of Educational ProgressNAEP...Ch. 10.1 - Prob. 2NAEP Ch. 10.1A - A second-grade class has a project to determine...Ch. 10.1A - Prob. 2A Ch. 10.1A - Prob. 3A

Knowledge Booster

Learn more about

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.

(a) To find: The mean and median of the sequences 2 , 4 , 6 , 8 , … , 200 , 1 , 3 , 5 , 7 , 9 , … , 199 and 5 , 13 , 21 , 29 , … , 157 .

Solution Summary: The author explains the arithmetic mean and median of the sequences 2,4,6,8,dots,200, 1,3,5,7,9 and 5,13,21,29,

Concept explainers

Videos

(a)

To find:

The mean and median of the sequences 2,4,6,8,…,200, 1,3,5,7,9,…,199 and 5,13,21,29,…,157.

(b)

To find:

The conjecture about the mean and the median of any arithmetic sequence.

Want to see the full answer?

Chapter 10 Solutions

(a) To find: The mean and median of the sequences 2 , 4 , 6 , 8 , … , 200 , 1 , 3 , 5 , 7 , 9 , … , 199 and 5 , 13 , 21 , 29 , … , 157 .

Solution Summary: The author explains the arithmetic mean and median of the sequences 2,4,6,8,dots,200, 1,3,5,7,9 and 5,13,21,29,

Concept explainers

Videos

(a) To find: The mean and median of the sequences 2,4,6,8,…,200, 1,3,5,7,9,…,199 and 5,13,21,29,…,157.

(b) To find: The conjecture about the mean and the median of any arithmetic sequence.

Want to see the full answer?

Chapter 10 Solutions

(a)

To find:

The mean and median of the sequences 2,4,6,8,…,200, 1,3,5,7,9,…,199 and 5,13,21,29,…,157.

(b)

To find:

The conjecture about the mean and the median of any arithmetic sequence.