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If the pth, qth, rth, and sth terms of a...

If the `pth`, `qth`, `rth`, and `sth` terms of an A.P. are in G.P., then `p-q ,q-r ,r-s` are in

A

A.P.

B

G.P.

C

H.P.

D

None of these

Text Solution

Verified by Experts

Given,

`pth`, `qth`, `rth`, and `sth` terms of an A.P

General term: `a_n=a+(n-1)d`

`T_p=a+(p−1)d`` \ \ \ ...(1)`

`T_q=a+(q−1)d`` \ \ \ ...(2)`

`T_r=a+(r−1)d`` \ \ \ ...(3)`

`T_s=a+(s−1)d`` \ \ \ ...(4)`

Equations `(1), (2), (3), (4)` are in GP

...
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
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  3. If the pth, qth, rth, and sth terms of an A.P. are in G.P., then p-q ,...

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  12. Insert 5 geometric means between 16 and 1/4

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  13. Insert 5 geometric means between (32)/9 and (81)/2

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  14. Find the geometric means of the following pairs of number: 2 and 8.

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  16. Find the geometric means of the following pairs of number: -8 and -2.

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  17. If a is the G.M. of 2 and 1/4, find a

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  18. Find the two numbers whose A.M. is 25 and GM is 20.

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  19. If A and G are respectively arithmetic and geometric mean between posi...

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  20. The sum of two numbers is 6 times their geometric mean, show that numb...

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