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Please, what is the formula for this quadratic sequence?The sequence is 6,26,54,90,134,186

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bossman98 | Student, Grade 9 | eNotes Newbie

Posted January 11, 2012 at 1:44 AM via web

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Please, what is the formula for this quadratic sequence?

The sequence is 6,26,54,90,134,186

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted January 11, 2012 at 2:32 AM (Answer #1)

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Find the difference between terms:

n2 - n1 = 20

n3 - n2 = 28

n4 - n3 = 36

n5 - n4 = 44

n6 - n5 = 52

Notice that the each difference increases by 8.  The coefficient of x^2 is half the the difference of the differences.  In this case, half of 8.  Therefore, a = 4.

y = 4x^2 + bx + c

 

Now select two points and substitute to find b and c.

Point1:  (1, 6)

6 = 4(1)^2 + b(1) + c

6 = 4 + b + c

2 = b + c

c = 2 - b

 

Point2:  (2, 26)

26 = 4(2)^2 + b(2) + c

26 = 16 + 2b + c

10 = 2b + c

c = 10 - 2b

 

Set these two equations equal to each other and solve for b.

2 - b = 10 - 2b

2 + b = 10

b = 8

 

Substitute 8 in for b and solve for c.

c = 2 - b

c = 2 - 8

c = -6

 

Solution:

y = 4x^2 + 8x + -6

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