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Show that each of one of the following p...

Show that each of one of the following progression is a G.P. Also, find the common ratio in each case: `a ,(3a^2)/4,(9a^3)/(16), ,`

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Let a = a, b = `(3a^2)/4`,
c = `(9a^3)/16` In GP,` b^2 = ac`
`(3a^2/4)^2 = 9a^3/16 × a`
`( 9a^4)/16= (9a^4)/16 `
So, the Common ratio = r =
`(3a^2/4)/a = (3a^2)/(4a) = (3a)/(4)`
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
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  6. Show that the sequence defined by an=2/(3^n),\ n in N\ is a G.P.

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  7. Find: the ninth term of the G.P. 1,4,16,64,………

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  8. Find: the 10th term of the G.P. -3/4,1/2,-1/3,2/9, dot

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  9. Find: the 8th term of the G.P. 0. 03 , 0.06 , 0.012 ,

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  10. Find: the 12th term of the G.P. 1/(a^3x^3),\ a x ,\ a^5x^5,\ dot

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  11. Find: n th term of the G.P. sqrt(3),1/(sqrt(3)),1/(3sqrt(3)),

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  12. Find: the 10th term of the G.P. sqrt(2),1/(sqrt(2)),1/(2sqrt(2)),

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  13. Find the 4th term from the end of the G.P. 2/(27),2/9,2/3, ,, , , ,...

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  14. Which term of the progression 0.004,0.02,0.1,… is 12.5.?

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  15. Which term of the G.P.: sqrt(2),1/(sqrt(2)),1/(2sqrt(2)),1/(4sqrt(2)),...

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  16. Which term of the G.P.: 2,\ 2\ sqrt(2),\ 4,\ doti s\ 128 ?

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  17. Which term of the G.P.: \ sqrt(3),3,3sqrt(3), i s\ 729 ?

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  18. Which term of the G.P.: 1/3,1/9,1/(27) i s1/(19683)?

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  19. Find the 4th term from the end of the G.P. 1/2,1/6,1/(18),1/(54), ,1/...

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  20. The fourth term of a G.P. is 27 and the 7th term is 729, find the G....

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