Home
Class 11
MATHS
If the pth, qth, rth, and sth terms of a...

If the pth, qth, rth, and sth terms of an A.P. are in G.P., then `p-q ,q-r ,r-s` are in a. A.P. b. G.P. c. H.P. d. none of these

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

If the pth, qth and rth terms of a G.P. are again in G.P., then p, q, r are in

If a ,b ,c are in A.P., the a/(b c),1/c ,1/b will be in a. A.P b. G.P. c. H.P. d. none of these

If a^2+b^2,a b+b c and b^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 p^(th), q^(th), r^(th) and s^(th) terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P.

If the pth, qth, and rth terms of an A.P. are in G.P., then the common ratio of the G.P. is a. (p r)/(q^2) b. r/p c. (q+r)/(p+q) d. (q-r)/(p-q)

If in a progression a_1, a_2, a_3,.......... e tc dot,(a_r-a_(r+1)) bears a constant ratio with a_rxxa_(r+1) , then the terms of the progression are in a. A.P b. G.P. c. H.P. d. none of these

If a x^3+b x^2+c x+d is divisible by a x^2+c ,t h e na ,b ,c ,d are in a. A.P. b. G.P. c. H.P. d. none of these

If the (m + 1)th, (n + 1)th and (r + 1)th terms of an A.P. are in G.P. and (1)/(m), (1)/(n), (1)/(r ) are in A.P., then find the ratio of the first term of the A.P. to its common difference in terms of n.

If 64, 27 , 36 are the Pth , Qth and Rth terms of a G.P., then P + 2Q is equal to

The pth , qth and rth terms of an A.P. are in G.P. Prove that the common ratio of the G.P. is (q-r)/(p-q) or (p-q)/(q-r)

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. In a G.P. the first, third, and fifth terms may be considered as the ...

    Text Solution

    |

  2. If a,b,c,d be in G.P. show that (b-c)^2+(c-a)^2+(d-b)^2=(a-d)^2.

    Text Solution

    |

  3. If the pth, qth, rth, and sth terms of an A.P. are in G.P., then p-q ,...

    Text Solution

    |

  4. A B C is a right-angled triangle in which /B=90^0 and B C=adot If n po...

    Text Solution

    |

  5. If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6,p!=1 , then the value ...

    Text Solution

    |

  6. ABCD is a square of length a, a in N, a > 1. Let L1, L2 , L3... be poi...

    Text Solution

    |

  7. Let Tr a n dSr be the rth term and sum up to rth term of a series, res...

    Text Solution

    |

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

    Text Solution

    |

  9. If a x^3+b x^2+c x+d is divisible by a x^2+c ,t h e na ,b ,c ,d are in...

    Text Solution

    |

  10. If the lines 3x + by + 5 = 0 and ax – 5y + 7 = 0 are perpendicular to ...

    Text Solution

    |

  11. In a geometric series, the first term is a and common ratio is rdot If...

    Text Solution

    |

  12. If x ,y ,a n dz are distinct prime numbers, then (a).x , y , a n dz ma...

    Text Solution

    |

  13. If x ,y , and z are in G.P. and x+3,y+3, and z+3 are in H.P., then a.y...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. The sum of first 15 terms of an A.P. is 750 and its first term is 15. ...

    Text Solution

    |

  17. The coefficient of x^(49) in the product (x-1)(x-3)(x-99)i s a. -99^...

    Text Solution

    |

  18. Let S=4/(19)+(44)/(19^2)+(444)/(19^3)+ u ptooo . Then s is equal to a....

    Text Solution

    |

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

    Text Solution

    |

  20. If the sum to infinity of the series 1+2r+3r^2+4r^3+ is 9/4, then val...

    Text Solution

    |