SOLUTION: What is the 100th term of the pattern 3a-4b, 4a-2b, 5a, 6a+2b, 7a+4b,....

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Question 1111836: What is the 100th term of the pattern 3a-4b, 4a-2b, 5a, 6a+2b, 7a+4b,....
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Every time we add  (a + 2b).


It is arithmetic progression with the first term  (3a-4b)  and the common difference  (a+2b).


The 100-th term is   a%5B100%5D = (3a-4b) + 99*(a+2b),


and you can simplify it further as far as you want.

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There is a bunch of lessons on arithmetic progressions in this site:
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions


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.