The given pattern continues. Write down the nth term of the sequence suggested by the pattern.
-$$\frac { 1 } { 1 } , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 } , \ldots$$
A) $a _ { n } = \frac { 1 } { 3 n - 2 }$
B) $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$
C) $a _ { n } = \frac { 1 } { n ^ { n - 1 } }$
D) $a _ { n } = \frac { 1 } { n ^ { 2 } }$

Question

Quizplus · Accepted Answer

The given sequence is of the form $\frac{1}{n^2}$, where $n$ is the position of the term in the sequence. This matches option D, $\frac{1}{n^2}$, as the denominators are perfect squares (1, 4, 9, 16, 25, ...) corresponding to the square of their position in the sequence (1^2, 2^2, 3^2, 4^2, 5^2, ...).

The Given Pattern Continues 11,14,19,116,125,…\frac { 1 } { 1 } , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 } , \ldots11​,41​,91​,161​,251​,…

The Given Pattern Continues $\frac { 1 } { 1 } , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 } , \ldots$