Question

find the 5th term.
t(n)=-4(2)^n=-128
find t(7)
t(n)=2(\frac{3}{2})^n

Explanation:

Step1: Find 5th - term

Substitute $n = 5$ into $t(n)=-4(2)^{n}$.
$t(5)=-4\times(2)^{5}$

Step2: Calculate exponent

$(2)^{5}=2\times2\times2\times2\times2 = 32$.
$t(5)=-4\times32$

Step3: Multiply

$-4\times32=-128$.

Step4: Find $t(7)$

Substitute $n = 7$ into $t(n)=2(\frac{3}{2})^{n}$.
$t(7)=2\times(\frac{3}{2})^{7}$

Step5: Calculate exponent

$(\frac{3}{2})^{7}=\frac{3^{7}}{2^{7}}=\frac{2187}{128}$.
$t(7)=2\times\frac{2187}{128}$

Step6: Simplify

$t(7)=\frac{2187}{64}$

Answer:

The 5th - term of $t(n)=-4(2)^{n}$ is $-128$ and $t(7)$ of $t(n)=2(\frac{3}{2})^{n}$ is $\frac{2187}{64}$