Question

I need help with all three questions please. I am just Stuck.

Answer 1

Answer:

$p_{o} = 6$, $r = 2$, $p_{12} = 24576$.

Step-by-step explanation:

The value of $p_{o}$ is the first value of the geometric series, that is, $p_{o} = 6$.

If the series represents a geometric sequence, then $r$ must be constant for every consecutive pair of elements, that is:

$r_{1} = \frac{p_{1}}{p_{o}} = \frac{12}{6} = 2$

$r_{2} = \frac{p_{2}}{p_{1}} = \frac{24}{12} = 2$

$r_{3} = \frac{p_{3}}{p_{2}} = \frac{48}{24} = 2$

Since $r_{1} = r_{2} = r_{3} = 2$, $r = 2$.

The geometric sequence can be represented by the following formula:

$p_{n} = p_{o}\cdot r^{n}$, for $n \in \mathbb{N}$

The 12th element of the geometric sequence is: ($p_{o} = 6$, $r = 2$, $n = 12$)

$p_{12} = 6\cdot 2^{12}$

$p_{12} = 24576$