SOLUTION: make a conjecture in terms of Q(n)(find the nth term) for the following sequence & then find the 100th term:n= 1 2 3 4 5 6 Q= 3 12 25

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Question 210252: make a conjecture in terms of Q(n)(find the nth term) for the following sequence & then find the 100th term:n= 1 2 3 4 5 6
Q= 3 12 25 42 63 88
Cannot figure out any part of this...I would really appreciate any help at this point!
Thanks!
Found 2 solutions by scott8148, stanbon:
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
the differences between consecutive Q terms are ___ 9, 13, 17, 21, 25

the difference between consecutive terms of the 1st set of differences is equal to 4 and is constant
___ this means that the conjecture is a second order expression (2nd differences constant)

Q(n) = an^2 + bn + c

Q(1) = a(1^2) + b(1) + c ___ 3 = a + b + c ___ 3 - a - b = c

Q(2) = a(2^2) + b(2) + c ___ 12 = 4a + 2b + c
substituting ___ 12 = 4a + 2b + 3 - a - b ___ 9 = 3a + b

Q(3) = a(3^2) + b(3) + c ___ 25 = 9a + 3b + c
substituting ___ 25 = 9a + 3b + 3 - a - b ___ 22 = 8a + 2b ___ 11 = 4a + b

subtracting equations ___ 2 = a

substituting ___ 11 = 4(2) + b ___ 3 = b

substituting ___ 3 - 2 - 3 = c ___ -2 = c

Q(n) = 2n^2 + 3n - 2

Q(100) = 2(100^2) + 3(100) - 2 = 20298

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
make a conjecture in terms of Q(n)(find the nth term) for the following sequence & then find the 100th term:
n= 1 2 3 4 5 6
Q= 3 12 25 42 63 88
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I ran a Quadratic regression program on the data
and got f(n) = 2n^2 + 3n -2
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f(100) = 2(100)^2 + 3(100) - 2 = 20298
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Cheers,
Stan H.