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Expert: Sherry Wallin - 12/10/2010


Question
Hello,
Could you please help me with this question?

Q: The rth term of an arithmetic progression is 1+4r. Find in therms of n, the sum of the n terms of the progression. (Answer given is n(2n+3))
Thank you!

Answer
Toon993~

The rth term can be considered the nth term so just replace the r with the n. The sum of n terms is S_n =(n/2)(a+a_n)

What you need to extrapolate from 1 + 4r is what is a?
Since you know the rth term you actually know as many of the terms you want. For example let r = 1: 1 + 4(1) = 5. This is the first term so it is a. a_n is 1 + 4n. Now put all this into the formula:
S_n = (n/2)(5 + 1 + 4n) = (n/2)(6 + 4n) = 2*(n/2)(3 + 2n) = n(2n + 3).

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Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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