Question 353260
First room is numbered with  d then numbers are:  d , (d+2),(d+4),.....

( to find next odd integer we add 2 , for example  3+2  = 5, 5 + 2 = 7 )



this is a series of arithmetic progression, where first term is d and

 common difference is  2 ....


now we have to find the sum of first seven terms 


to find sum of first n terms, we use  Sn = ( n/2 )  * { 2a + (n-1)d }

where n :  no. of terms
  
      a :  the first term

      d : the common difference


here n = 7, a = d (according to question) , d = 2



S7= (7/2) * { 2d + (7-1)*2}

  = (7/2)  * { 2d + 12 }

  =  (7/2) * 2 { d + 6}

  = 7{d + 6}

   = 7d + 42



sum = 7d + 42 
  


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