Question #1f6de

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Question #1f6de

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Answer 1 · 2017-02-21T11:34:42

$a_{4} = a_{3} \times 6 = 144 \times 6 = 864$ $a_4=a_3xx6 " "=" " 144xx6 " "=" " 864$

$a_{5} = a_{5} \times 6 = 864 \times 6 = 5184$ $a_5=a_5xx6" "=" "864xx6" "=" "5184$

$a_{6} = a_{5} \times 6 = 5184 \times 6 = 31122$ $a_6=a_5xx6" "=" "5184xx6" "=" " 31122$

Explanation:

Let the term count be $i$ $i$
Let the ith term be $a_{i}$ $a_i$

So we have:
$i = 1 \to a_{i} = a_{1} = 4$ $i=1->a_i =a_1=4$
$i = 2 \to a_{i} = a_{2} = 24$ $i=2->a_i=a_2=24$
$i = 3 \to a_{i} = a_{3} = 144$ $i=3->a_i=a_3=144$

The question states this is a geometric sequence.

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

$Determine the value of r$ $color(brown)("Determine the value of "r)$

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

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

Thus $r = 6$ $r=6$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Determine the next three terms$ $color(brown)("Determine the next three terms")$

The last known term is $a_{3} = 144$ $a_3=144$

so we have:

$a_{4} = a_{3} \times 6 = 144 \times 6 = 864$ $a_4=a_3xx6 " "=" " 144xx6 " "=" " 864$

$a_{5} = a_{5} \times 6 = 864 \times 6 = 5184$ $a_5=a_5xx6" "=" "864xx6" "=" "5184$

$a_{6} = a_{5} \times 6 = 5184 \times 6 = 31122$ $a_6=a_5xx6" "=" "5184xx6" "=" " 31122$

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Question #1f6de

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