Home
Class 11
MATHS
A sequence a1,a2,a3, ... is defined by ...

A sequence `a_1,a_2,a_3, ... ` is defined by letting `a_1=3 ` ` a n d ` `a_k=7a_(k-1)` for natural numbers `k ,kgeq2.` Show that `a_n=3.7_n-1` for all `n in N` .

Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUATIONS

    RD SHARMA ENGLISH|Exercise All Questions|163 Videos

  • MATHEMATICAL REASONING

    RD SHARMA ENGLISH|Exercise All Questions|182 Videos

Similar Questions

Explore conceptually related problems

A sequence a_(1),a_(2),a_(3), . . . is defined by letting a_(1)=3 and a_(k)=7a_(k-1) , for all natural numbers k≥2 . Show that a_(n)=3*7^(n-1) for natural numbers.

A sequence d_(1),d_(2),d_(3) . . . is defined by letting d_(1)=2 and d_(k)=(d_(k-1))/(k), for all natural numbers, k≥2 . Show that d_(n)=(2)/(n!) , for all n in N .

Let sequence by defined by a_1=3,a_n=3a_(n-1)+1 for all n >1

A sequence of number a_1, a_2, a_3,…..,a_n is generated by the rule a_(n+1) = 2a_(n) . If a_(7) - a_(6) = 96 , then what is the value of a_(7) ?

Find the first four terms of the sequence defined by a_1=3\ a n d\ a_n=3a_(n-1)+2 , for all n >1.

Find the first four terms of the sequence defined by a_1=3\ a n d\ a_n=3a_(n-1)+2 , for all n .1.

A sequence of positive integers a_1 , a_2, a_3, …..a_n is given by the rule a_(n + 1) = 2a_(n) + 1 . The only even number in the sequence is 38. What is the value of a_2 ?

If a_1, a_2, a_3,.....a_n are in H.P. and a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1 a_n , then k is equal to

Let a sequence be defined by a_1=1,a_2=1 and a_n=a_(n-1)+a_(n-2) for all n >2, Find (a_(n+1))/(a_n) for n=1,2,3, 4.

A sequence a_n , n in N be an A.P. such that a_7 = 9 and a_1 a_2 a_7 is least, then the common difference is:

RD SHARMA ENGLISH-MATHEMATICAL INDUCTION-All Questions
  1. Prove that for n in N ,10^n+3. 4^(n+2)+5 is divisible by 9 .

    Text Solution

    |

  2. Prove by induction that the sum of the cubes of three consecutive n...

    Text Solution

    |

  3. A sequence a1,a2,a3, ... is defined by letting a1=3 a n d ak=7a(k-...

    Text Solution

    |

  4. A sequence x1, x2, x3,.... is defined by letting x1=2 and xk=x(k-1)...

    Text Solution

    |

  5. Show by the Principle of Mathematical induction that the sum Sn, of th...

    Text Solution

    |

  6. Prove that the number of subsets of a set containing n distinct elemen...

    Text Solution

    |

  7. Using the principle of mathematical induction prove that : 1. 3+2. ...

    Text Solution

    |

  8. Prove by the principle of mathematical induction that for all n in N ...

    Text Solution

    |

  9. Using the principle of mathematical induction prove that 1+1/(1+2)...

    Text Solution

    |

  10. Prove by induction that the sum Sn=n^3+3n^2+5n+3 is divisible by 3 for...

    Text Solution

    |

  11. Using the principle of mathematical induction prove that 1/(1. 2. ...

    Text Solution

    |

  12. Using the principle of mathematical induction. Prove that (x^(n)-y^(n...

    Text Solution

    |

  13. Using the principle of mathematical induction prove that 41^n-14^n ...

    Text Solution

    |

  14. Using the principle of mathematical induction, prove that (2^(3n)-1) i...

    Text Solution

    |

  15. Using principle of mathematical induction prove that sqrtn<1/sqrt1+1/s...

    Text Solution

    |

  16. Prove that: 1+2+3+....+ n<((2n+1)^2)/8 for all ""n in Ndot

    Text Solution

    |

  17. Prove that: 1^2+2^2+3^2.....+n^2>(n^3)/3,n in N

    Text Solution

    |

  18. A sequence x0, x1,x2,x3, ddot is defined by lettingx0=5 and xk=4+x(k-1...

    Text Solution

    |

  19. Prove by the principle of mathematical induction that n<2^n"for all"n ...

    Text Solution

    |

  20. Prove by the principle of mathematical induction that for all n in N ...

    Text Solution

    |