Question

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

Answer 1

9514 1404 393

Answer:

• x = 5
• y = 13

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

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The explicit formula for the sequence is ...

an = n^2 -2n +5