What's the rule for the sequence: \( \frac{1}{16}, \frac{1}{8}, \frac{3}{16}, \frac{1}{4}, \frac{5}{16}, \frac{3}{8} \)?
Answer (2)
The rule is that you add 1/16 each time. You can see this if you find the common denominator (16):
1/16, 2/16, 3/16, 4/16, 5/16, 6/16
The sequence 16 1 , 8 1 , 16 3 , 4 1 , 16 5 , 8 3 can be described by the rule a n = 16 n for n = 1 , 2 , 3 , 4 , 5 , 6 , indicating that each term is derived from increasing the numerator by 1 while keeping the denominator constant at 16. This shows a simple linear relationship in the sequence. The common pattern observed is that each term increments by 1 in the numerator when expressed over a common denominator.
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