If a1=1 and an+1=4+3an3+2an,n≥1 and if limn→∞ an=a, then the value of a, is

If a1=1 and an+1=4+3an3+2an,n1 and if limnan=a, then the value of a, is

  1. A

    2

  2. B

    2

  3. C

    2

  4. D

    none of these

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    Solution:

    We have,

    an+1=4+3an3+2anlimnan+1=limn4+3an3+2ana=4+3a3+2a, where a=limxan 2a2=4a=±2

    But, a2 because each an>0 for all n.

    Hence a = 2.

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