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The terms of an infinitely decreasing G....

The terms of an infinitely decreasing `G.P.` in which all the terms are positive, the first term is `4` and the difference between the third and fifth term is `81/32` , then find the common ratio.

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Given, `a=4`
General term `=ar^(n-1)`
Third term `=ar^2`
Fifth term `=ar^4`
Given, `ar^2-ar^4=32/81`
`r^2=t`
`4t-4t^2=32/81`
`81t-81t^2=8`
...
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
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  2. Prove that: 2^(1/4).4^(1/8), 8^(1/16). 16^(1/32)......... oo=2.

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  9. Show that in an infinite G.P. with common ratio r(|r|<1) , each term b...

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  14. If a,b,c are in G.P. and a^(1/x)=b^(1/y)=c^(1/z) prove that x, y, z ar...

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  15. If a^2+b^2,a b+b c and b^2+c^2 are in G.P., then a ,b ,c are in

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  16. If a , b , c are in G.P. prove that loga , logb , logc are in A.P.

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  17. If a ,\ b ,\ c are in G.P. prove that 1/((log)a m),1/((log)b m),1/((lo...

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  18. Find k such that k+9, k-6 and 4 from three consecutive terms of a G.P.

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  19. Three numbers are in A.P. and their sum is 15. If 1,3,9 be added to th...

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  20. The sum of three numbers which are consecutive terms of an A.P. is 21....

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