Find formula for the $n^{t h}$ term of the sequence assuming that the indicated pattern continues: $\frac{1}{8}, \frac{- 4}{17}, \frac{9}{26}, \frac{- 16}{35}, . . .$

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Solution

Explanation to correct answer:
Finding formula for the $n^{t h}$ term:
Given sequence is $\frac{1}{8}, \frac{- 4}{17}, \frac{9}{26}, \frac{- 16}{35}, . . .$
We can notice that the value of numerator is a perfect square or negative of a perfect square in even terms
That is numerator is ${(- 1)}^{n + 1} n^{2}$ where $n$ is its position
Denominator is an arithmetic sequence starting from $8$ with common difference $9$
Therefore $n^{t h}$ term is $a_{n} = \frac{{(- 1)}^{n + 1} n^{2}}{8 + (n - 1) 9}$

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Find formula for the nth term of the sequence assuming that the indicated pattern continues:18,-417,926,-1635,...

Find formula for the $n^{t h}$ term of the sequence assuming that the indicated pattern continues: $\frac{1}{8}, \frac{- 4}{17}, \frac{9}{26}, \frac{- 16}{35}, . . .$