Calculate the Sum of Odd Integers from 15 to 240 | Find the Answer Now!

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Homework Help Overview

The problem involves calculating the sum of odd integers greater than 15 and less than 241, specifically focusing on the arithmetic properties of the sequence of odd numbers within that range.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the arithmetic progression of odd integers, questioning how to apply the formula for the sum and the properties of averages in this context. There are attempts to identify the first and last terms and their average, as well as the total count of terms in the series.

Discussion Status

Several participants have provided insights into the nature of the problem, including the use of arithmetic progression properties and sigma notation. There is an ongoing exploration of different methods to approach the summation without reaching a definitive conclusion.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is an emphasis on understanding the underlying concepts rather than simply calculating an answer.

whitehorsey
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1. Find the sum of the odd integers greater than 15 but less than 241.
a. 14,336
b. 28,672
c. 14,448
d. 28896




2. an = a1 + (n-1)*d



3. I know that n = 8 and a1= 17 and d = 2. But I don't know how to get one of these answers:
14,336
28,672
14,448
28896
 
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It's an arithmetic progression. Look it up. Or try adding (17+19+...+237+239) to (239+237+...+19+17) term by term and draw your own conclusions.
 
One way to find a sum of numbers is to find their average value of the numbers, then multiply by how many numbers there are.

A very nice property of arithmetic progressions is that the average of all the numbers in the progression is the same as the average of the first and last numbers only. What is the first number in this progression? What is the last? What is their average? How many numbers are there?
 
If you have been introduced to sigma (summation) notation you can also write the progression of odd numbers as,

[tex]\sum2n+1[/tex]

where the sum ranges from 8 to 119. Same idea really. You have a basic formula for the arithmetic progression, which HalllsofIvy gave you in words.
 

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