In a quadratic sequence.....Term 2 is 11,Term 4 is -7,term 7 is -64....determin the general term for the sequence
4a + 2b + c = 11
16a + 4b + c = -7
49a + 7b + c = -64
(a,b,c) = (-2,3,13)
So, Tn = -2n^2 + 3n + 13
How dd u fynd dem....lyk de steps
just solved the system of equations. I used wolframalpha.com, but you can use elimination, determinants, substitution, or whatever you like to use for solving systems of equations.
Algebra I stuff. Dust off those skills.
To determine the general term for a quadratic sequence, we need to find a pattern in the terms. We can start by finding the common difference between consecutive terms.
First, let's calculate the differences between the terms:
Difference between Term 2 and Term 1: 11 - ? = 11
Difference between Term 3 and Term 2: ? - 11 = ?
Difference between Term 4 and Term 3: -7 - ? = ?
Difference between Term 5 and Term 4: ? - (-7) = ?
Difference between Term 6 and Term 5: ? - ? = ?
Difference between Term 7 and Term 6: -64 - ? = ?
From the given information, we have:
Difference between Term 2 and Term 1: 11 - ? = 11 --> ? = 0
Difference between Term 4 and Term 3: -7 - 0 = -7 --> ? = -7
Difference between Term 7 and Term 6: -64 - ? = -7 --> ? = -57
We observe that the differences are not constant, so this is not an arithmetic sequence. However, if we calculate the differences between the differences, we might find a pattern:
Difference between the Differences:
Difference between (Term 4 - Term 3) and (Term 3 - Term 2): -7 - 11 = -18
Difference between (Term 5 - Term 4) and (Term 4 - Term 3): ? - (-18) = ?
Difference between (Term 6 - Term 5) and (Term 5 - Term 4): ? - ? = ?
Difference between (Term 7 - Term 6) and (Term 6 - Term 5): ? - ? = ?
From the given information, we have:
Difference between (Term 4 - Term 3) and (Term 3 - Term 2): -7 - 11 = -18 --> ? = -18
Difference between (Term 5 - Term 4) and (Term 4 - Term 3): ? - (-18) = ? --> ? = -39
Difference between (Term 6 - Term 5) and (Term 5 - Term 4): ? - ? = ? --> ? = -21
Now, let's assume that the general term for the quadratic sequence is given by the formula:
Term(n) = an^2 + bn + c
We can substitute the values we know into the equation and solve for a, b, and c using the three given terms:
Term(2) = a(2)^2 + b(2) + c = 11
4a + 2b + c = 11 (1)
Term(4) = a(4)^2 + b(4) + c = -7
16a + 4b + c = -7 (2)
Term(7) = a(7)^2 + b(7) + c = -64
49a + 7b + c = -64 (3)
We now have a system of three equations (1), (2), and (3) with three unknowns (a, b, c). Solving this system of equations will give us the values of a, b, and c, allowing us to determine the general term for the sequence.