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Let S be the set of all integers that can be written as 2n2 − 6n, where n is a nonzero integer. Which of the following integers is in S?
- a)6
- b)30
- c)46
- d)64
- e)80
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
Let S be the set of all integers that can be written as 2n2 − 6n...
To solve this problem, start with n = 1 until you reach an answer choice: when you reach n = 8, you will get 2(8)2 − 6(8) = 80, answer choice E.
Community Answer
Let S be the set of all integers that can be written as 2n2 − 6n...
The set S can be written as S = {2n^2 | n ∈ Z}, where Z represents the set of all integers.
In other words, S is the set of all integers that can be obtained by multiplying 2 with the square of an integer.
For example, if we substitute n = 0, 1, -1, 2, -2, etc., into the equation 2n^2, we get the following values:
S = {2(0)^2, 2(1)^2, 2(-1)^2, 2(2)^2, 2(-2)^2, ...}
= {0, 2, 2, 8, 8, ...}
So, the set S contains all even integers (including zero) and can be expressed as S = {..., -8, -2, 0, 2, 8, ...}.
In other words, S is the set of all integers that can be obtained by multiplying 2 with the square of an integer.
For example, if we substitute n = 0, 1, -1, 2, -2, etc., into the equation 2n^2, we get the following values:
S = {2(0)^2, 2(1)^2, 2(-1)^2, 2(2)^2, 2(-2)^2, ...}
= {0, 2, 2, 8, 8, ...}
So, the set S contains all even integers (including zero) and can be expressed as S = {..., -8, -2, 0, 2, 8, ...}.
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Let S be the set of all integers that can be written as 2n2 − 6n, where n is a nonzero integer. Which of the following integers is in S?a)6b)30c)46d)64e)80Correct answer is option 'E'. Can you explain this answer?
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