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Solution: The sequence is $ a, a+d, a+2d, a+3d, a+4d $. The middle term is $ a+2d = 5 $, so:
From (1): $ a = 5 - 2d $. Substitute into (2):
Question: An ichthyologist studying coral reef fish populations models the population trend with the equation $
Multiply both sides by $ x - 2 $, assuming $ x
$$Question: Find the cubic polynomial $ h(x) $ such that $ h(1) = 3 $, $ h(2) = 12 $, $ h(3) = 27 $, and $ h(4) = 48 $.
For $ x = 1 $: $ a + b + c + d = 3 $
For $ x = 2 $: $ 8a + 4b + 2c + d = 12 $
For $ x = 3 $: $ 27a + 9b + 3c + d = 27 $
For $ x = 4 $: $ 64a + 16b + 4c + d = 48 $
$ 7a + 3b + c = 9 $ (from 2nd - 1st)