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Please help with Arithmetic Sequence Question

  1. May 27, 2014 #1
    1. The problem statement, all variables and given/known data

    * "/" means divided by *

    1/a , 1/b , 1/c are consecutive terms in an AS, where a,b,c ε R\0. (whatever that means haha)

    express b in terms of a and c. give your answer in its simplest form.

    *thats all it says*

    2. Relevant equations

    there are none :)

    3. The attempt at a solution

    sorry but i have absolutely no clue and thats why im posting this haha
     
  2. jcsd
  3. May 27, 2014 #2
    ok nevermind guys sorry, i just found that i did do the question haha................

    anyways for those who wanna know its like this...

    T1, T2, T3
    1/a, 1/b, 1/c = AS
    T2-T1=T3-T2
    T2+T2=T3+T1
    1/b + 1/b = 1/c + 1/a
    2(1/b)=1/ac
    2b=1/(1/a - 1/c)
    b= 2 1/(1/a - 1/c)

    and thats it i think..
     
  4. May 27, 2014 #3

    adjacent

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    Gold Member

    It's wrong.
    ##\frac{1}{c}+\frac{1}{a} \neq \frac{1}{ac}##
    You have some algebra problems there. I get a different answer. Try again
    I have coloured the wrong parts in red.
     
  5. May 27, 2014 #4

    adjacent

    User Avatar
    Gold Member

    Please post your correct solution too,for other to see :smile:
     
  6. May 27, 2014 #5
    so what is the rest of it that you got? because im stumped haha
     
  7. May 27, 2014 #6

    adjacent

    User Avatar
    Gold Member

    Let's start from the original question.
    ##\frac{1}{a},\frac{1}{b},\frac{1}{c}## . Express b interms of a and c.
    As you showed, ##\frac{1}{b}-\frac{1}{a}=\frac{1}{c}-\frac{1}{b}##
    So ##\frac{1}{b}+\frac{1}{b}=\frac{1}{c}+\frac{1}{a}##
    ##\frac{2}{b}=\frac{1}{c}+\frac{1}{a}##


    Simplify ##\frac{1}{c}+\frac{1}{a}## then solve for b.
     
  8. Jun 2, 2014 #7
    ok thanks haha, i have it now, i even checked with my A- standard student/friend :D
     
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