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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.

A

A.P.

B

G.P.

C

H.P.

D

none of these

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The correct Answer is:
B
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If a , b and c b respectively the pth , qth and rth terms of an A.P. prove that a(q-r) +b(r-p) +c (p-q) =0

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If a , b ,and c are respectively, the pth, qth , and rth terms of a G.P., show that (q-r)loga+(r-p)logb+(p-q)logc=0.

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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Chapter Test
  1. The maximum sum of the series 20+19 1/3+18 2/3+ is 310 b. 300 c. 0320 ...

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  2. If three numbers are in G.P., then the numbers obtained by adding the ...

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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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  4. Let a,b,c be three positive prime number. The progrrssion in which sqr...

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  5. If 1/(b-a)+1/(b-c)=1/a+1/c , then (A). a ,b ,a n dc are in H.P. (B). a...

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  6. If three numbers are in H.P., then the numbers obtained by subtracting...

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  7. The first three of four given numbers are in G.P. and their last three...

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  8. In a G.P. of positive terms if any terms is equal to the sum of next ...

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  9. If a,b,c are in H.P and ab+bc+ca=15 then ca=

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  10. If sum(r=1)^(oo)(1)/((2r-1)^(2))=(pi^(2))/(8), then sum(r=1)^(oo) (1)/...

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  11. It is given that 1/1^4 + 1/2^4 +1/3^4 … to oo= pi^4/90 , then 1/1^4...

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  12. The minimum number of terms from the beginning of the series 20+22(2)/...

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  13. The sum of the series 1-3+5-7+9-11+ . . . . To n terms is

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  14. If three positive unequal numbers a, b, c are in H.P., then

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  15. If the fifth term of a G.P. is 2, then write the product of its 9 t...

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  16. 1^3-2^3+3^3-4^3+........+9^3 is equal to

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  17. The sum of infinite number of terms in G.P. is 20 and the sum of their...

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  18. If 1, log (9) (3^(1 - x) + 2) and log(3) (4.3^(x) -1) are A.P. then...

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  19. Two sequences lta(n)gtandltb(n)gt are defined by a(n)=log((5^(n+1))/...

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  20. The sum of the series (1)/(sqrt(1)+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1...

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