Subjects algebra

Sequence Term D340F3

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1. The problem asks us to find the 8th term of the sequence defined by the formula $$T(n) = \frac{n - 2}{n^2 - 2}$$. 2. To find the 8th term, substitute $n = 8$ into the formula: $$T(8) = \frac{8 - 2}{8^2 - 2}$$ 3. Simplify the numerator and denominator: $$T(8) = \frac{6}{64 - 2}$$ $$T(8) = \frac{6}{62}$$ 4. Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is 2: $$T(8) = \frac{\cancel{6}^3}{\cancel{62}^{31}}$$ 5. The simplest form of the 8th term is: $$T(8) = \frac{3}{31}$$ Therefore, the 8th term of the sequence is $\frac{3}{31}$.