Problem 7
Answers:
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Step-by-step explanation:
In step 1, there are 2 dots. So that number (2) fills in the blank for dots A.
Step 2 has 5 dots, which fills in the blank for dots B.
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Problem 8
Answer: A) Quadratic
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Step-by-step explanation:
We have this sequence of dots: {1, 2, 5, 10, ...}
Note the increments of +1, +3, +5, ...
The increments aren't the same, so we don't have a linear sequence. But because the increment amounts go up by 2 each time, this strongly implies a quadratic sequence.
The rule for this sequence is n^2 + 1. Whatever the step number (n) is, we square it and add 1 onto that result. For instance, for step 3, we have n = 3 that leads to n^2 + 1 = 3^2 + 1 = 9 + 1 = 10. Also, note how the lone dot on the left of step 3 is tacked onto the 3 by 3 square of dots.
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Problem 9
Answers:
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Step-by-step explanation:
Same idea as problem 7
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Problem 10
Answer: B) Exponential
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Step-by-step explanation:
The sequence is {1, 3, 9, 27, ...}
In step 3 we have 3 rows and 9 columns of dots to give 3*9 = 27 dots total here.
The sequence is growing by a factor of 3 each time. In other words, we are tripling the terms or multiplying each term by 3 to get the next term.
Therefore, we have an exponential pattern.
The rule is 3^n
Eg: if we're on step n = 2, then we have 3^n = 3^2 = 9 dots.