Question

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

Explanation:

Step1: Find the 5th term of $t(n)=-4(2)^n$

Substitute $n = 5$ into the formula: $t(5)=-4\times(2)^5$.

Step2: Calculate $(2)^5$

$(2)^5=2\times2\times2\times2\times2 = 32$.

Step3: Calculate $t(5)$

$t(5)=-4\times32=-128$.

Step4: Find $t(7)$ for $t(n)=2(\frac{3}{2})^n$

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

Step5: Calculate $(\frac{3}{2})^7$

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

Step6: Calculate $t(7)$

$t(7)=2\times\frac{2187}{128}=\frac{2187}{64}$.

Answer:

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