41 tuning forks are so arranged that every fork gives 5beats with the next. The last fork has a frequency that is double of the first. The frequency of first fork is

Given

     Number of forks=41

     Number of beats=5

41 Tuning forks arranged in series in increasing order of frequency.

Each fork gives ‘5’ beats with the preceeding one means, frequency of each fork is ‘5’ more than the preceeding one

   Hence 41 frequencies are in arithmetic progression with common difference is -5hz

 It is given that the frequency of last one $f_{41}$  is double of first one $f_1$

 We know formula $f_n=f_1+\left(n-1\right)d$ .

         $f_n=f_{41}$    $f_n=2f_1$   n=41 ,d=5

                  $f_{41}=2f_1$

          $2f_1=f_1+\left(41-1\right)5$

            $f_1=40\times 5$

       $\therefore f_1=200Hz$