Question

find five consecutive terms in AP whose sun is 520 and product of first and the last to the product of second and fourth in 20:21

Answer 1

let the terms be a - 4d , a - 2d , a , a +2d , a - 4d
given a - 4d + a - 2d + a + a +2d + a - 4d = 520
   5a = 520 
  a = 104
     

so given that [( a - 4d ) (a - 4d)]/[ (a - 2d)  (a +2d )] = 20/21
so solving for d after putting the value of a 
we get d = 6.5
so the terms are  a - 4×6.5 , a - 2×6.5 , a , a +2×6.5 , a - 4×6.5
that is 

104 - 4×6.5, 104 - 2×6.5 , 104, 104 +2×6.5 , 104 - 4×6.5
that  is  78, 91 , 104 , 117 , 130