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If the 2nd difference of a quadratic pattern is ""4"" what does the ""n squared"" sequence become?

a) 2n²
b) 4n²
c) 6n²
d) 8n²

User Shl
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1 Answer

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Final answer:

The 2nd difference of "4" in a quadratic pattern indicates that the n squared sequence becomes 2n², as the second difference is twice the value of the 'a' coefficient in the quadratic expression an² + bn + c.

Step-by-step explanation:

If the 2nd difference of a quadratic pattern is "4", to find out what the n squared sequence becomes, we need to realize that the 2nd difference in a quadratic sequence corresponds to the coefficient of the n² term when the sequence is expressed in the form an² + bn + c. Given that the 2nd difference is 4, this implies that the coefficient 'a' is 2 (since the 2nd difference is twice the value of 'a' in the general quadratic expression). Therefore, the n squared sequence becomes 2n².

The process of identifying this involves observing a pattern in the sequence of numbers and recognizing that the second difference is constant for quadratic sequences. In essence, for a second difference of 4, we are looking at a sequence that increases by 4 more than the previous increase each time. The coefficient of the n² term is half the second difference, so we end up with 2n² as the n squared term in the equation.

User Shadox
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