Answer:
6. neither; f(n) = n³; f(4) = 64; f(10) = 1000
7. neither; g(n) = 8n³; g(4) = 512; g(10) = 8000
Step-by-step explanation:
6.
The differences between the numbers in the sequence 1, 8, 27 are 7, 19, so are not constant. The ratios of successive terms are 8, 3 3/8, so are not constant, either. Thus the sequence is neither arithmetic (an addition patterns) or geometric (a multiplication pattern).
These numbers are a sequence of cubes, as the pictures show. They are 1³, 2³, 3³. So the n-th term in the sequence will be ...
f(n) = n³
Then the 4th and 10th terms are ...
f(4) = 4³ = 64
f(10) = 10³ = 1000
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7.
The method and logic for the kind of sequence are the same as for Sequence 6. It is neither an addition or multiplication pattern.
The edge of the cube in this sequence is 2n, so the sequence rule is ...
g(n) = f(2n) = (2n)³ = 2³×n³
g(n) = 8n³
Each term of this sequence is 8 times the corresponding term of the previous sequence.
g(4) = 8×64 = 512
g(10) = 8×1000 = 8000
