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Three positive numbers form an increasin...

Three positive numbers form an increasing GP. If the middle term in this GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is

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The correct Answer is:
`r=2+sqrt3`
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CBSE COMPLEMENTARY MATERIAL-SEQUENCES AND SERIES -SECTION-D (LONG ANSWER TYPE QUESTIONS )
  1. Prove that the sum of n numbers between a and b such that then(a + b)r...

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  2. A square is drawn by joining the mid points of the sides of a square. ...

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  3. If a, b, c are in G.P., then prove that (1)/(a^(2)-b^(2))-(1)/(b^(2)-c...

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  4. Find two positive numbers whose difference is 12 an whose A.M. exce...

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  5. If a is A.M. of b and c and c,G(1),G(2),b are in G.P., then find the v...

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  6. Find the sum of the series,1.3.4 + 5.7.8 + 9.11.12 +.............. upt...

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  7. Evaluatesum1^10(2r-1)^2

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  8. The sum of an infinite GP is 57 and the sum of their cubes is 9747. Fi...

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  9. If (10)^9 + 2(11)^1 (10)^8 + 3(11)^2 (10)^7+...........+10 (11)^9= k ...

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  10. The sum of the first n terms of the series (1)/(2)+(3)/(4)+(7)/(8)+(15...

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  11. Three positive numbers form an increasing GP. If the middle term in th...

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  12. If a,b,c are in AP, show that 1/((sqrtb+sqrtc)),1/((sqrtc+sqrta)),1/...

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  13. Find the sum of the series 1-3/2+5/4-7/8+9/16..........oo

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  14. In the sum of first n terms of an A.P. is cn^2, then the sum of square...

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  15. Let pa n dq be the roots of the equation x^2-2x+A=0 and let ra n ds be...

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  16. If S(1), S(2), S(3),...,S(n) are the sums of infinite geometric series...

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  17. If the m th, n th and p th terms of an AP and GP are equal and are x ,...

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  18. The sum of an infinite GP is 57 and the sum of their cubes is 9747. Fi...

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  19. Find three numbers in G.P. whose sum is 13 and the sum of whose square...

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