Home
Class 11
MATHS
Consider a sequence {an }with a1=2 and a...

Consider a sequence `{a_n }with a_1=2 and a_n=(a_(n-1)^ 2)/(a_(n-2))` for all `ngeq3,` terms of the sequence being distinct. Given that `a_1 and a_5` are positive integers and`a_5lt=162` then the possible value(s) of `a_5` can be (a) 162 (b) 64 (c) 32 (d) 2

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

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.

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

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.

Let {a_n}(ngeq1) be a sequence such that a_1=1,a n d3a_(n+1)-3a_n=1 for all ngeq1. Then find the value of a_(2002.)

The Fibonacci sequence is defined by 1=a_1=a_2 and a_n=a_(n-1)+a_(n-2,)n > 2. Find (a_(n+1))/(a_n),for n=5.

Consider the sequence defined by a_n=a n^2+b n+cdot If a_1=1,a_2=5,a n da_3=11 , then find the value of a_(10)dot

Write the first three terms of the sequence defined by a_1= 2,a_(n+1)=(2a_n+3)/(a_n+2) .

Let {a_n}(ngeq1) be a sequence such that a_1=1,a n d3a_(n+1)-3a_n=1fora l lngeq1. Then find the value of a_(2002.)

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If 1/(b-a)+1/(b-c)=1/a+1/c , then (A). a ,b ,a n dc are in H.P. (B). a...

    Text Solution

    |

  2. If a ,b ,a n dc are in G.P. and x a n d y , respectively, be arithmeti...

    Text Solution

    |

  3. Consider a sequence {an }with a1=2 and an=(a(n-1)^ 2)/(a(n-2)) for all...

    Text Solution

    |

  4. Which of the following can be terms (not necessarily consecutive) of ...

    Text Solution

    |

  5. The numbers 1, 4, 16 can be three terms (not necessarily consecutive) ...

    Text Solution

    |

  6. Each question has four choices a,b,c and d out of which only one is...

    Text Solution

    |

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

    Text Solution

    |

  8. If b(n+1)=1/(1-bn)forngeq1a n db1=b3, t h e nsum(r=1)^(2001)b r^ 2001 ...

    Text Solution

    |

  9. Let a1, a2, a3, ,a(100) be an arithmetic progression with a1=3a n dsp...

    Text Solution

    |

  10. If 1^2+2^2+3^2++2003^2=(2003)(4007)(334) and (1)(2003)+(2)(2002)+(3)(2...

    Text Solution

    |

  11. The value of sum(i=1)^nsum(j=1)^isum(k=1)^j1=220 , then the value of ...

    Text Solution

    |

  12. The sum of 0. 2+0.004+0. 00006+0. 0000008+... to oo is a.(200)/(891) ...

    Text Solution

    |

  13. If tn=1/4(n+2)(n+3) for n=1, 2 ,3,.... then 1/t1+1/t2+1/t3+....+1/(t(...

    Text Solution

    |

  14. The coefficient of x^(19) in the polynomial (x-1)(x-2)(x-2^2)(x-2^(19)...

    Text Solution

    |

  15. If 1-1/3+1/5-1/7+1/9-1/(11)+=pi/4 , then value of 1/(1xx3)+1/(5xx7)+1/...

    Text Solution

    |

  16. The positive integer n for which 2xx2^2+3xx2^3+4xx2^4+......+nxx2^n=2...

    Text Solution

    |

  17. If tn denotes the nth term of the series 2+3+6+11+18+...then t(50)...

    Text Solution

    |

  18. The number of positive integral ordered pairs of (a ,b) such that 6,a ...

    Text Solution

    |

  19. Let a ,b >0, let 5a-b ,2a+b ,a+2b be in A.P. and (b+1)^2, a b+1,(a-1)^...

    Text Solution

    |

  20. The difference between the sum of the first k terms of the series ...

    Text Solution

    |