Using only the numbers 4 through 12, fill in the circles so that the numbers on each straight line add up to 21

The correct numbers to fill the given circles from 4 to 12 so that each straight line adds up to give a sum of 21 would be as follows:

4 in the center, 5 above it and 12 below it.

10 and 6 to the left and right of 5 respectively.

9 and 8 to the left and right of 4 at the center.

12 at the bottom(just below the center 4) and 11 and 7 to the left and the right of 12 at the bottom.

To verify,

We can add up each straight line if we get 21 as the sum or not.

The center line(CL)  = 5 + 4 + 12 = 21

The horizontal line passing through the center(HL) = 9 + 4 + 8 = 21

The North-West line(NW) = 10 + 4 + 7 = 21

The North-East line(NE) = 6 + 4 + 11 = 21

The diagram has been attached for clarity.

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f(x) is going down by 4

step-by-step explanation:

(its either that or its going left by 4)

10 - 8 = -2

  8 - 6 = -2

etc, so -2 is the common difference

step-by-step explanation: