Question

Find a formula for the general term an of the sequence (starting with a1): {-4/25,5/36,-6/49,7/64,...}

Answer 1

\[\begin{align*}
a_1&=\frac{(-1)^1(1+3)}{(1+4)^2}=-\frac{4}{25}\\
a_2&=\frac{(-1)^2(2+3)}{(2+4)^2}=\frac{5}{36}\\
\vdots\\
a_n&=\cdots
\end{align*}\]