# Question #1f6de

Feb 21, 2017

${a}_{4} = {a}_{3} \times 6 \text{ "=" " 144xx6 " "=" } 864$

${a}_{5} = {a}_{5} \times 6 \text{ "=" "864xx6" "=" } 5184$

${a}_{6} = {a}_{5} \times 6 \text{ "=" "5184xx6" "=" } 31122$

#### Explanation:

Let the term count be $i$
Let the ith term be ${a}_{i}$

So we have:
$i = 1 \to {a}_{i} = {a}_{1} = 4$
$i = 2 \to {a}_{i} = {a}_{2} = 24$
$i = 3 \to {a}_{i} = {a}_{3} = 144$

The question states this is a geometric sequence.

Let the expression for the term be ${a}_{i} {r}^{n}$
Where $r$ is the common ratio and $n$ is some variant (function) of $i$

$\textcolor{b r o w n}{\text{Determine the value of } r}$

$\frac{24}{4} = 6$

$\frac{144}{24} = 6$

Thus $r = 6$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b r o w n}{\text{Determine the next three terms}}$

The last known term is ${a}_{3} = 144$

so we have:

${a}_{4} = {a}_{3} \times 6 \text{ "=" " 144xx6 " "=" } 864$

${a}_{5} = {a}_{5} \times 6 \text{ "=" "864xx6" "=" } 5184$

${a}_{6} = {a}_{5} \times 6 \text{ "=" "5184xx6" "=" } 31122$