If $a_1, a_2, a_3 …………$ an are in $A.P$ and $a_1 + a_4 + a_7 + …………… + a_{16} = 114$, then $a_1 + a_6 + a_{11} + a_{16}$ is equal to

  • [JEE MAIN 2019]
  • A

    $76$

  • B

    $64$

  • C

    $98$

  • D

    $38$

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In an $A.P.,$ if $p^{\text {th }}$ term is $\frac{1}{q}$ and $q^{\text {th }}$ term is $\frac{1}{p},$ prove that the sum of first $p q$ terms is $\frac{1}{2}(p q+1),$ where $p \neq q$

After inserting $n$, $A.M.'s$ between $2$ and $38$, the sum of the resulting progression is $200$. The value of $n$ is

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The houses on one side of a road are numbered using consecutive even numbers. The sum of the numbers of all the houses in that row is $170$ . If there are at least $6$ houses in that row and $a$ is the number of the sixth house, then

  • [KVPY 2014]

The sum of $n$ arithmetic means between $a$ and $b$, is