Write an expression for the nth term of the sequence. $9 , - \frac { 9 } { 4 } , \frac { 9 } { 9 } , - \frac { 9 } { 16 } , \mathrm {~L}$
A) $\frac { 9 - 1 ^ { n + 1 } } { n ^ { 2 } }$
B) $\frac { 9 ( - 1 ) ^ { n } } { n ^ { 2 } }$
C) $\frac { 9 ( - 1 ) ^ { n - 1 } } { n ^ { 2 } }$
D) $\frac { - 1 ^ { n - 1 } } { 9 n ^ { 2 } }$
E) $\frac { ( - 1 ) ^ { n } } { 9 n ^ { 2 } }$

Question

Quizplus · Accepted Answer

The sequence alternates in sign, which is represented by $(-1)^{n-1}$, starting positive. The denominator increases by squares of natural numbers, and the numerator remains 9. Thus, the nth term is $\frac{9(-1)^{n-1}}{n^2}$.

Write an Expression for the Nth Term of the Sequence 9,−94,99,−916, L9 , - \frac { 9 } { 4 } , \frac { 9 } { 9 } , - \frac { 9 } { 16 } , \mathrm {~L}9,−49​,99​,−169​, L

Write an Expression for the Nth Term of the Sequence $9 , - \frac { 9 } { 4 } , \frac { 9 } { 9 } , - \frac { 9 } { 16 } , \mathrm {~L}$