The second difference 4;x;8;y;20; is 2​

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Step-by-step explanation:

First differences are ...

  x -4, 8 -x, y -8, 20 -y

Then second differences are ...

  (8 -x) -(x -4)

  (y -8) -(8 -x)

  (20 -y) -(y -8)

Each of these is said to be 2, so we have ...

  12 -2x = 2   ⇒   x = 5

  28 -2y = 2   ⇒   y = 13

And an equation we can use to check:

  x +y -16 = 2   ⇒   5 +13 -16 = 2 . . . . true

The explicit formula for the sequence is ...

  an = n^2 -2n +5

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.