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If p ,q ,r are in A.P., show that the pt...

If `p ,q ,r` are in A.P., show that the pth, qth and rth terms of any G.P. are in G.P.

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ATQ,
p, q and r are in A.P
` => 2q=p+r`
General term of G.P is `T(n)=a r^(n−1)`
`P^th` term is : `T(p)=a r^(p−1)`...(1)
`q^th` term is : `T(q)=a r^(q−1)`...(2)
`r^th` term is : `T(r)=a r^(R−1)`...(3)
To prove: `T(p),T(q),T(r)` are in G.P
...
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
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  3. If p ,q ,r are in A.P., show that the pth, qth and rth terms of any G....

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

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

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

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  14. The product of three numbers in G.P. is 216. If 2, 8, 6, be added to ...

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  15. Find the sum of 10 terms of the G.P. 3, 6, 12,...

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  16. In an increasing G.P. , the sum of the first and the last term is 66, ...

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  17. If S1,S2a n dS3 be respectively the sum of n, 2n and 3n terms of a G....

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

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

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  20. Find the sum of an infinitely decreasing G.P. whose first term is equa...

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