If $n$ arithmetic means are inserted between a and $100$ such that the ratio of the first mean to the last mean is $1: 7$ and $a+n=33$, then the value of $n$ is

  • [JEE MAIN 2022]
  • A

    $21$

  • B

    $22$

  • C

    $23$

  • D

    $24$

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  • [IIT 2011]