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Question

Insert 5 geometric means between 329 and 812.


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    Solution

    Let G1,G2,G3,G4,G5 be 5 geometric means between 329 and 812

    Then, 329,G1,G2,G3,G4,G5,812 is a G.P.

    with a=329,b=812

    r=(ba)1n+1

    =(812329)15+1=(812×932)16=(3626)=32

    Thus, G1=ar=329×32=163

    G2=ar2=329×94=8

    G3=ar3=329×278=12

    G4=ar4=329×3424=2times9=18

    G5=ar5=329×3525=27

    Hence, 163,8,12,18,27 are 5 geometric means

    between 329 and 812.


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