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If the first & the (2n + 1)th terms of a...

If the first & the (2n + 1)th terms of an A.P. , a G.P & an H.P. of positive terms are equal and their (n + 1)th terms are a, b & c respectively , then

A

a = b = c

B

`a ge b ge c`

C

a + c = 2b

D

`ac = b^2`

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The correct Answer is:
A, B, D
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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
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  2. The sides of a right angle triangle from a G.P. the tangent of the sma...

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  3. If the first & the (2n + 1)th terms of an A.P. , a G.P & an H.P. of po...

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  4. If the arithmetic mean of two positive numbers a & b (a gt b) is twice...

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  5. If Sn denotes the sum to n terms of the series (1 le n le 9) 1 + 22 + ...

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  6. If a , b , c are in H.P. , then

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  7. Let S1 , S2,,,,, be squares such that for each n ge 1 the length of a ...

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  8. Given a sequence t1 , t2 ,..... if its possible to find a function f(r...

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  9. Given a sequence t1 , t2 ,..... if its possible to find a function f(r...

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  10. Let a1, a2 , a3,...., am be the arithmetic means between -2 and 1027 a...

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  11. Let a1, a2 , a3,...., am be the arithmetic means between -2 and 1027 a...

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  12. If A, G and H are respectively arithmetic , geometric and harmonic mea...

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  13. If A, G and H are respectively arithmetic , geometric and harmonic mea...

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  14. Let a1,a2 ,a3 ...... be an A.P. Prove that sum(n=1)^(2m)(-1)^(n-1)an^2...

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  15. A three digit number whose consecutive digits from a G.P. If we subtra...

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  16. If an denotes the coefficient of x^n in P(x) = (1 + x+ 2x^2 + 3x^3 +.....

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  17. Two consecutive numbers from 1,2,3,.....,n are removed, then arithmeti...

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  18. The value of xyz is 55 or 343/55 according as the sequence a, x, y, z,...

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  19. If a, b, c are in HP and if ((a + b)/(2a - b)) + ((c + b)/(2c - b)) gt...

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  20. If alpha1 , alpha2, ......, alphan are in A.P, whose common difference...

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