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The given quadratic sequence is:
\[
-4, -8, -10, -10, -8
\]
We need to find an expression for the \( n \)-th term, \( T_n \), of the sequence. Since it's a quadratic sequence, we know the formula will be of the form:
\[
T_n = an^2 + bn + c
\]

### Step 1: First and second differences
Start by calculating the first and second differences.

1st differences:
\[
-8 - (-4) = -4, \quad -10 - (-8) = -2, \quad -10 - (-10) = 0, \quad -8 - (-10) = 2
\]
So, the first differences are: \( -4, -2, 0, 2 \).

2nd differences:
\[
-2 - (-4) = 2, \quad 0 - (-2) = 2, \quad 2 - 0 = 2
\]


Here are the first five terms of a quadratic sequence: -4, -8, -10, -10, -8. Find an expression, in terms of n, for the nth term of the sequence.

Solve the quadratic sequence problem where the first five terms are -4, -8, -10, -10, -8. Learn how to use first and second differences to find the nth term formula T_n = an^2 + bn + c. Suitable for students in Grades 9-11.

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