The sum of 4 consecutive terms of an AP is 26 and their product is 880,find the four numbers.

Question

From the maths branch of Arithmetic Progressions...

Answer 1

The terms in an Arithmetic Progression have a common difference, d.

 

Let the four terms be:

     x  (x+d)    (x+2d)    (x+3d)

 

The sum is 26:

      x + (x+d) + (x+2d) + (x+3d) = 26

      4x + 6d = 26

      2x + 3d = 13       [note:  already guessing that x=2 and d=3 is reasonable;    2, 5, 8, 11]

 

Their product is:

     x(x+d)(x+2d)(x+3d) = 880     [the prime factors of 880 are:   2, 2, 2, 2, 5, 11]

                            If the four terms are integers, try 2, 5, 2*2*2, 11;      that is, 2, 5, 8, 11]