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The 5th, 8th and 11th terms of a G.P. ar...

The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that `q^(2)=ps.`

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`a_5​=p=a_1​r^4`
`a_8​=q=a_1​r^7`
`a_1​1=s=a_1​r^10`
`q^2=a_1^2​r^(14 )`
`q^2=a_1​r^4.a_1​r^(10)`
`q^2=ps`
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. The 7th term of a G.P. is 8 times the 4th term and the 5th term is 4...

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  2. If the G.Ps 5 , 10, 20, and 1280, 640, 320 have their nth terms equ...

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  3. The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Sh...

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  4. The 4th term of a G.P. is square of its second term and the first t...

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  5. In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th t...

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  6. If a ,\ b ,\ c ,\ d\ a n d\ p are different real numbers such that: (a...

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  7. If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0) , then show tha...

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  8. the sum of three numbers in G.P. is 56. If we subtract 1,7,21 from the...

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  9. Find three numbers in G.P. whose sum is 65 and whose product is 3375.

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  10. If the sum of three numbers in G.P. is 38 and their product is 1728, ...

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  11. The sum of first three terms of a G.P. is 13/12 and their product is ...

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  12. The product of the three numbers in G.P. is 125 and sum of their pr...

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  13. The sum of first three terms of a G.P. is (39)/(10) and their product ...

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  14. The sum of three numbers in G.P. is 14. If the first two terms are eac...

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  15. Find three numbers in G.P. whose product is 729 and the sum of their ...

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  16. The sum of three numbers in G.P. is 21 and the sum of their squares is...

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  17. Find the sum of 7 terms of the G.P. 3,6,12…

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  18. Find the sum of 7 terms of the sequence (1/5+2/(5^2)+3/(5^3)),\ (1/(5^...

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  19. Find the sum of the series 2+6+18++4374

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  20. The sum of first three terms of a G.P is 16 and the sum of the next th...

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