Home
Class 11
MATHS
Show that the sequence loga, log(ab), lo...

Show that the sequence `loga, log(ab), log(ab^2), log(ab^3)`,.....is in A.P

Text Solution

Verified by Experts

`loga, log(ab), log(ab)^2,log(ab^3),......`
`log(ab)-loga=log((ab)/a)=logb`
`log(ab^2)-log(ab)=log((ab^2)/(ab))=logb.`
`log(ab^3)-log(ab^2)=log((ab^3)/(ab^2))=logb`
Threfore`There exists a common difference
`therefore`The given series is in A.P
Promotional Banner

Topper's Solved these Questions

  • RECTANGULAR CO-ORDINATES

    PATHFINDER|Exercise QUESTION BANK|27 Videos

  • SEQUENCES AND SERIES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

Show that the sequence loga ,log(a b),log(a b^2),log(a b^3), is an A.P. Find the nth term.

The sequence log a, log a^2/b , log a^3/b^2 , ..... is

The sequence log a, log (a^(2)/b), log (a^(3)/b^(2)) is:

The value of loga b-log|b|=

Show that log_(2)log_(2)log_(2) 16=1

Prove that : (viii) (log_(a)x)/(log_(ab)x) = 1+log_(a)b .

If x is a positive real number different from 1 such that log_(a)^(x),log_(b)^(x),log_(c)^(x) are in A.P , then

If log2,log(2^n-1) and log(2^n+3) are in A.P. then n =

Show that log_(3)log_(2)log_(sqrt3)81 = 1

If a_(n)( gt 0) be the n^(th) term of a G.P. then |(log a_(n), log a_(n+1), log a_(n+2)),(log a_(n+3), loga_(n+4),log a_(n+5)),(log a_(n+6),log a_(n+7), log a_(n+8))| is equal to

PATHFINDER-SAME SPECIAL SEQUENCE-QUESTION BANK
  1. Find the sum of 41,36,31.....to 12terms.

    Text Solution

    |

  2. How many terms are there in the A.P.7,10,13,......,43?

    Text Solution

    |

  3. Show that the sequence loga, log(ab), log(ab^2), log(ab^3),.....is in ...

    Text Solution

    |

  4. If the m^(th) term and the n^(th) term of an A.P. are respectively (1)...

    Text Solution

    |

  5. Determine the number of terms in the A.P.3,7,11,......,407.Also find i...

    Text Solution

    |

  6. In a certain A.P the 24th term is twice the 10th term. Prove that the...

    Text Solution

    |

  7. The sum of three numbers in A.P is 12 and sum of their cubes is 288. F...

    Text Solution

    |

  8. Find the sum first 24 terms of A.P. a1,a2,a3,..........., if it is kn...

    Text Solution

    |

  9. If the P^(th)and q^(th)terms of an A.Pare a and b respectively,then sh...

    Text Solution

    |

  10. If s1 be the sum of (2n+1) terms of an A.P and s2 be the sum its odd t...

    Text Solution

    |

  11. The ratio if the sum of n terms of two A.P,s is (7n+1):(4n+27). Find t...

    Text Solution

    |

  12. If a^2, b^2, c^2 are in A.P , then prove that 1/(b+c), 1/(c+a),1/(a+b)...

    Text Solution

    |

  13. Find the sum of the following series 6+66+666+..........to n term

    Text Solution

    |

  14. If the first and the n^("th") term of a G.P. are a and b, respectivel...

    Text Solution

    |

  15. Find the equations of the lines, which cut-off intercepts on the axes ...

    Text Solution

    |

  16. If S1, S2 and S3 be respectively the sum of n, 2n and 3n terms of a G....

    Text Solution

    |

  17. If S be the sum. P be the product,and R the sum of the reciprocals of ...

    Text Solution

    |

  18. If x = 1+a+a^2+..........oo where abs(a)lt1 and y=1+b+b^2+........oowh...

    Text Solution

    |

  19. Prove that : (2^(1/4)cdot4^(1/8)cdot8^(1/16)cdot16^(1/32)......oo)=2

    Text Solution

    |

  20. Find the value of n so that (a^(n+1)+b^(n+1))/(a^(n)+b^n) may be the ...

    Text Solution

    |