A series of book was published at seven years intervals when the seventh book was published the total sum of publication year was 13, 1524. first book was published in?

• First of all total sum of publication years is 13524 not 131524.
  Let the first year is x.
  so the years are x, x+7, x+14, x+21, x+28, x+35 and x+42.
  Now Sum of all years = (n/2)(2a+(n-1)d) [n=number of years, a=first year, d=difference of two years]
  =(7/2)(2x+(7-1)7)
  =7x+147
  Again Sum of all years = 13524
  So, 7x+147=13524
  => x=1911
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• let the 1st year be x and each book is published at the interval of 7 years and no of books are 7. so last book will be published on (x+42) yrs
  as
  sum=n/2 (a+l)
  where n=no of books
  a=x (as we have assumed)
  l= x+42
  putting these values
  7/2 (x+x+42)=13524 (not 131524)
  x=1911
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