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The largest block size that divides both 18 and 42 evenly is the greatest common divisor of 18 and 42.
An archaeologist finds a sequence of inscriptions dated every 3 years starting from year $ 3 $, up to and including year $ 198 $. How many inscriptions are there?
5x + 4 + 2x + 11 + 3x + 7 = 10x + 22
---Question: Let $ f(x) $ be a cubic polynomial such that $ f(1) = 10 $, $ f(2) = 20 $, $ f(3) = 34 $, and $ f(4) = 58 $. Find $ f(5) $.
Solution: Since $ f(x) $ is a cubic polynomial, its third differences are constant. We compute the values:
Since the third differences are constant (assumed for a cubic), we extend the pattern:
Add $ 16 $ to the second difference $ 24 $, giving $ 40 $. Then first difference becomes $ 24 + 40 = 64 $. Thus,
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