Home
Class 12
MATHS
If a,b, and c are in G.P then a+b,2b and...

If a,b, and c are in G.P then a+b,2b and b+ c are in

A

A.P

B

G.P

C

H.P

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let a=1,b=2,c=4 Then,
`a+b=3,2b=4,b+c=6`
`rArr1/4-1/3=-1/12` and `1/6-1/4=-1/12`
Hence, a+b,2b,b+c are in H.P.
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise (Multiple & Comprehension)|66 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise EXERCIESE ( MULTIPLE CORRECT ANSWER TYPE )|2 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.9|9 Videos

  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

If a,b, and c are in A.P and b-a,c-b and a are in G.P then a:b:c is

If a , b ,a n dc are in G.P., then a+b ,2b ,a n db+c are in a. A.P b. G.P. c. H.P. d. none of these

a,b,c,d in R^+ such that a,b and c are in H.P and ap.bq, and cr are in G.P then p/r+t/p is equal to

If a ,b ,c are in G.P. and a-b ,c-a ,a n db-c are in H.P., then prove that a+4b+c is equal to 0.

For any three positive real numbers a, b and c, 9(25a^2+b^2)+25(c^2-3ac)=15b(3a+c) Then: (1) b, c and a are in G.P. (2) b, c and a are in A.P. (3) a, b and c are in A.P (4) a, b and c are in G.P

For any three positive real numbers a, b and c, 9(25a^2+b^2)+25(c^2-3ac)=15b(3a+c) Then: (1) b, c and a are in G.P. (2) b, c and a are in A.P. (3) a, b and c are in A.P (4) a, b and c are in G.P

If a , b, c, … are in G.P. then 2a,2b,2c,… are in ….

If 1/(b-a)+1/(b-c)=1/a+1/c , then A. a ,b ,a n dc are in H.P. B. a ,b ,a n dc are in A.P. C. b=a+c D. 3a=b+c

If a^2+b^2,a b+b c ,a n db^2+c^2 are in G.P., then a ,b ,c are in a. A.P. b. G.P. c. H.P. d. none of these

If a, b, c, d are in G.P., then (a + b + c + d)^(2) is equal to

CENGAGE-PROGRESSION AND SERIES-Exercise (Single)
  1. a,b,c,d in R^+ such that a,b and c are in H.P and ap.bq, and cr are in...

    Text Solution

    |

  2. If in a progression a1, a2, a3, e t cdot,(ar-a(r+1)) bears a constant...

    Text Solution

    |

  3. If a,b, and c are in G.P then a+b,2b and b+ c are in

    Text Solution

    |

  4. If a,x,b are in A.P.,a,y,b are in G.P. and a,z,b are in H.P. such that...

    Text Solution

    |

  5. Let n in N ,n > 25. Let A ,G ,H deonote te arithmetic mean, geometric...

    Text Solution

    |

  6. If A.M., G.M., and H.M. of the first and last terms of the series of 1...

    Text Solution

    |

  7. If H1.,H2,…,H20 are 20 harmonic means between 2 and 3, then (H1+2)/(H1...

    Text Solution

    |

  8. If the sum of n terms of an A.P is cn (n-1)where c ne 0 then the sum o...

    Text Solution

    |

  9. If bi=1-ai na = Sigma(i=1)^(n) ai, nb = Sigma(i=1)^(n) bi " then " Si...

    Text Solution

    |

  10. The sum 1+3+7+15+31+...to100 terms is 2^(100)-102 b b. 2^(99)-101 c. ...

    Text Solution

    |

  11. Consider the sequence 1,2,2,4,4,4,8,8,8,8,8,8,8,8,... Then 1025th term...

    Text Solution

    |

  12. The value of Sigma(i=1)^(n) Sigma(j=1)^(i) underset(k=1)overset(j) =22...

    Text Solution

    |

  13. If 1^2+2^2+3^2++2003^2=(2003)(4007)(334)a n d(1)(2003)+(2)(2002)+(3)(2...

    Text Solution

    |

  14. If tn denotes the nth term of the series 2+3+6+11+18+….. Then t50 is

    Text Solution

    |

  15. The sum of series Sigma(r=0)^(r) (-1)^r(n+2r)^2 (where n is even) is

    Text Solution

    |

  16. If(1^2-t1)+(2^2-t2)+….+(n^2-tn)=(n(n^2-1))/(3) then tn is equal to

    Text Solution

    |

  17. If (1+3+5++p)+(1+3+5++q)=(1+3+5++r) where each set of parentheses cont...

    Text Solution

    |

  18. If Hn=1+12++1/ndot , then the value of Sn=1+3/2+5/3++(99)/(50) is H(50...

    Text Solution

    |

  19. The sum to 50 terms of the series 3/1^2+5/(1^2+2^2)+7/(1^+2^2+3^2)+...

    Text Solution

    |

  20. Let S=4/19+44/(19)^2+444/(19)^3+...oo then find the value of S

    Text Solution

    |