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

    $24$

Similar Questions

If $a_m$ denotes the mth term of an $A.P.$ then $a_m$ =

If $a,\,b,\,c$ are in $A.P.$, then $(a + 2b - c)$ $(2b + c - a)$ $(c + a - b)$ equals

Let $a_{1}, a_{2}, \ldots \ldots, a_{21}$ be an $A.P.$ such that $\sum_{n=1}^{20} \frac{1}{a_{n} a_{n+1}}=\frac{4}{9}$. If the sum of this AP is $189,$ then  $a_{6} \mathrm{a}_{16}$ is equal to :

  • [JEE MAIN 2021]

Find the $20^{\text {th }}$ term in the following sequence whose $n^{\text {th }}$ term is $a_{n}=\frac{n(n-2)}{n+3}$ 

The number of terms in the series $101 + 99 + 97 + ..... + 47$ is