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.

12th Edition

ISBN: 9780137657988

Author: BILLSTEIN

Publisher: INTER PEAR

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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.

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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.

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Chapter 10.4B, Problem 11A

Chapter 10.4B, Problem 13A

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(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,

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(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.