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

Algebra ->  Sequences-and-series -> 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       Log On

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.