SOLUTION: Determine the sum of the following series (hint: the answer will have the variable 𝑘): 4𝑘 + 11𝑘 + 18𝑘 + ⋯ + 74𝑘 I NEED HELP ASAP!! THANKS

Algebra ->  Sequences-and-series -> SOLUTION: Determine the sum of the following series (hint: the answer will have the variable 𝑘): 4𝑘 + 11𝑘 + 18𝑘 + ⋯ + 74𝑘 I NEED HELP ASAP!! THANKS      Log On


   



Question 1181940: Determine the sum of the following series (hint: the answer will have the variable 𝑘):
4𝑘 + 11𝑘 + 18𝑘 + ⋯ + 74𝑘
I NEED HELP ASAP!! THANKS

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

The sum is the AVERAGE of the first term and the last term, taken   %2874-4%29%2F7%2B1 = 70%2F7%2B1 = 10+1 = 11 times.


The average of the first and the last terms is  %284k+%2B+74k%29%2F2 = %2878k%29%2F2 = 39k.



So the total sum is  (39k)*11 = 429k.      ANSWER

Solved.


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This problem is on Arithmetic progressions.


For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.