SOLUTION: Hello Online Tutors! Here's my question: If a5=100 and a11=10 are the two terms of an arithmetic sequence, then what is the value of a9? Thanks to anyone who can help! Amelia

Question 1111179: Hello Online Tutors! Here's my question:
If a5=100 and a11=10 are the two terms of an arithmetic sequence, then what is the value of a9?
Thanks to anyone who can help!
Amelia B
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.

You have 

 =  = 100,       (1)


 =  = 10.      (2)


Subtract eq(1) from eq(2)  (both sides).  You will get

10d - 4d = 10 - 100,

6d = -90

d =  = -15.


Therefore,   =  = 10 - (-15) = 10 + 15 = 25.

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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

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