Home
Class 11
MATHS
Consider the ten numbers a r ,a r^2, a r...

Consider the ten numbers `a r ,a r^2, a r^3, ..... ,a r^(10)dot` If their sum is 18 and the sum of their reciprocals is 6, then the product of these ten numbers is a.`81` b. `243` c. `343` d.` 324`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

Consider the ten numbers a r ,a r^2, a r^3, ,a r^(10)dot If their sum is 18 and the sum of their reciprocals is 6, then the product of these ten numbers is 81 b. 243 c. 343 d. 324

If S be the sum, p the product and R the sum of the reciprocals of n terms of a G.P., then (S/R)^n is equal to

if S is the sum , P the product and R the sum of reciprocals of n terms in G.P. prove that P^2 R^n=S^n

if S is the sum , P the product and R the sum of reciprocals of n terms in G.P. prove that P^2 R^n=S^n

If S is the sum, P the product and R the sum of the reciprocals of n terms in G.P., prove that P^(2)= ((S)/(R))^(n) .

If S be the sum P the product and R be the sum of the reciprocals of n terms of a GP then p^2 is equal to S//R b. R//S c. (R//S)^n d. (S//R)^n

Let S be the sum, P the product, and R the sum of reciprocals of n terms in a G.P. Prove that P^2R^n=S^ndot

Find the sum of the products of the ten numbers +-1,+-2,+-3,+-4,a n d+-5 taking two at a time.

In a triangle ABC if sides a = 13, b =14 and c = 15, then reciprocals of r_(1),r_(2),r_(3) are in the ratio

Statement-1: the sum of the diigits in the ten's place of all numbers formed with the help of 3,4,5,6 taken all at a time is 108. Statement-2: The sum of the digits in the ten's place= The sum of the digits is the units's place.

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If a ,b ,c are digits, then the rational number represented by odotc a...

    Text Solution

    |

  2. If a = underset(55 "times")underbrace(111.....1), b= 1+10+10^(2)+10^(3...

    Text Solution

    |

  3. Consider the ten numbers a r ,a r^2, a r^3, ..... ,a r^(10)dot If the...

    Text Solution

    |

  4. The sum of 20 terms of a series of which every even term is 2 times ...

    Text Solution

    |

  5. Let an be the nth term of a G.P. of positive numbers. Let sum(n=1)^(10...

    Text Solution

    |

  6. If the pth, qth, and rth terms of an A.P. are in G.P., then the common...

    Text Solution

    |

  7. In a G.P. the first, third, and fifth terms may be considered as the ...

    Text Solution

    |

  8. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. 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

    |

  16. The line x+ y = 1 meets X-axis at A and Y-axis at B,P is the mid-poin...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. If x ,y , and z are in G.P. and x+3,y+3, and z+3 are in H.P., then y=2...

    Text Solution

    |

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

    Text Solution

    |