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If a ,b ,c are in G.P., then prove that ...

If `a ,b ,c` are in G.P., then prove that `loga^n ,logb^n ,logc^n` are in A.P.

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Here, `a,b and c` are in G.P.
`:. b^2 = ac`
Taking log both sides,
`log(b^2) = log(ac)`
`=>2logb = loga+logc`
`=>n*2logb = nloga+nlogc`
`=>2logb^n = loga^n+logc^n`
`:. loga^n,logb^n and logc^n` are in A.P.
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
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  2. If a ,b ,c ,d are in G.P., prove that a+b,b+c ,c+d are also in G.P.

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  3. If a ,b ,c are in G.P., then prove that loga^n ,logb^n ,logc^n are in ...

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  9. If each term of an infinite G.P. is twice the sum of the terms foll...

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  10. If |x|<1a n d|y|<1, find the sum of infinity of the following series:...

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  12. Find the sum to n terms of the sequence given by an=sum2^n,n in Ndot

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  13. Sum the series : x(x+y)+x^2(x^2+y^2)+x^3(x^3+y^3+ ton terms.

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  14. Find the sum of the following series : 0. 7+0. 77+0. 777+ ton term...

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  19. Determine the number of terms in G.P. ifa1=3,an=96 and Sn=189.

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  20. How many terms of the geometric series 1+4+16+64+ will make the sum 54...

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