Explanation Given Information: Natural numbers from 1 to 99. Formula used: The sum of first n terms of an arithmetic sequence is given by s n = n 2 ( a 1 + a n ) , the n th term is given by a n = a 1 + ( n − 1 ) d and the common difference d is given by d = a n + 1 − a n for any positive integer n ≥ 1 . Calculation: The odd numbers from 1 to 99 can be represented in the form of an arithmetic sequence, 1 , 3 , 5 , 7 , … 99 Here, the first term a 1 = 1 . The common difference d can be calculated by the formula d = a n + 1 − a n For n = 1 , d = a 1 + 1 − a 1 = a 2 − a 1 = 3 − 1 = 2 Now, apply the formula a n = a 1 + ( n − 1 ) d for a 1 = 1 , d = 2 and a n = 99 and solve for n : a n = a 1 + ( n − 1 ) d 99 = 1 + ( n − 1 ) 2 Subtract 1 from both sides: 99 = 1<

7th Edition

ISBN: 9780134494807

Author: BITTINGER

Publisher: PEARSON CO

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Chapter 14.2, Problem 38ES

To determine

To calculate: The sum of the odd numbers from 1 to 99 (inclusive).

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Chapter 14.2, Problem 37ES

Chapter 14.2, Problem 39ES

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Chapter 14 Solutions

EP ELEMENTARY+INTERMEDIATE ALG.-MYMATHA

Ch. 14.1 - Prob. 1YT Ch. 14.1 - Prob. 2YT Ch. 14.1 - Prob. 3YT Ch. 14.1 - Prob. 4YT Ch. 14.1 - Prob. 5YT Ch. 14.1 - Prob. 1CYU Ch. 14.1 - Prob. 2CYU Ch. 14.1 - Prob. 3CYU Ch. 14.1 - Prob. 4CYU Ch. 14.1 - Prob. 5CYU

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