Question

What is a formula for the nth term of the given sequence?192, -144, 108...

Answer 1

Given the sequence 192, -144, 108...

`\begin{gathered} \text{ r=}(-144)/(192)=-0.75 \\ r=(108)/(-144)=-0.75 \end{gathered}`

The sequence has a common ratio. It is a geometric sequence.

the nth term of a Geometric sequence is given by the formula

`\begin{gathered} T_n=ar^(n-1) \\ \text{Where a = 192, r=-0.75=-3/4} \\ T_n=192((-3)/(4))^(n-1) \\ T_n=192\text{ x }((-3)/(4))^n.\text{ }((-3)/(4))^(-1) \\ =192\text{ x }((-3)/(4))^{n\text{ }}\text{ (}(-4)/(3)) \\ =192((-4)/(3))((-3)/(4))^n \\ =-256((-3)/(4))^n \\ \\ \text{Hence, The nth term is }-256((-3)/(4))^n \end{gathered}`