close
    If a5= 48 qnd a17=196608 are the terms of a goemetric sequence find a32

    0  Views: 535 Answers: 2 Posted: 11 years ago

    2 Answers

    a5 = 48
    a17 = 196,608
    a32 = ?

    Geometric Formula: an = a1*r^n-1
    a1 = 1st term
    r = common ratio
    n = sequence term you're finding

    Write two equations using the 5th and 32nd terms from the formula.

    Equation 1:

    a5 = [ a1*r^5-1 = 48]
    a5 = a1*r^4 = 48

    Equation 2:

    a17 = [ a1*r^17-1 = 196,608 ]
    a17 = a1*r^16 = 196,608

    Divide equation 2 by equation 1 to find common ratio.

    a1*r^16 = 196,608 / a1*r^4 = 48

    r^12 = 4096
    r = +-2

    Find the 1st term using either equation.

    a1*r^4 = 48

    16a1/16 = 48/16

    a1 = 3

    Now, find the 32nd term. There will be two answers.

    an = a1*r^n-1
    a32 = 3*2^32-1
    a32 = 3(2)^31
    a32 = 3(2,147,483,648)
    a32 = 6,442,450,944

    a32 = 3*-2^32-1
    a32 = 3(-2)^31
    a32 = 3(-2,147,483,648)
    a32 = -6,442,450,944

    Check: an = a1*r^n-1 > common ratio is +-2

    a1 = 3

    a1 = 3(2)^1-1
    a1 = 3(2)^0
    a1 = 3(1)
    a1 = 3

    a1 = 3(-2)^1-1
    a1 = 3(-2)^0
    a1 = 3(1)
    a1 = 3



    a5 = 48

    a5 = 3(2)^5-1
    a5 = 3(2)^4
    a5 = 3(16)
    a5 = 48

    a5 = 3(-2)^5-1
    a5 = 3(-2)^4
    a5 = 3(16)
    a5 = 48

    a17 = 196,608

    a17 = 3(2)^17-1
    a17 = 3(2)^16
    a17 = 3(65,536)
    a17 = 196,608

    a17 = 3(-2)^17-1
    a17 = 3(-2)^16
    a17 = 3(65,536)
    a17 = 196,608

    country bumpkin

    Moderator
    As Bob said, Oh come on! (*~*)
    Your knowledge of math is amazing. My son is starting college in a couple of months and he's dreading the math course because he always had so much trouble understanding math.
    chelleanne

    I'm refreshing my memory by looking at these kids math homework. Tell your son that he can find math help by going on YouTube. Math tutors/teachers put up videos with math problems and explanation on solving for all types of math problems.
    country bumpkin

    Moderator
    I'll let him know. Thanks (*~*)

    Oh, come on.   



    Top contributors in Uncategorized category

     
    ROMOS
    Answers: 18064 / Questions: 154
    Karma: 1101K
     
    Colleen
    Answers: 47271 / Questions: 115
    Karma: 953K
     
    country bumpkin
    Answers: 11323 / Questions: 160
    Karma: 838K
     
    Benthere
    Answers: 2393 / Questions: 30
    Karma: 760K
    > Top contributors chart

    Unanswered Questions

    449065
    questions
    718197
    answers
    724235
    users