Question 195098

Find the missing term of each geometric sequence. 
<pre><font size = 4 color = "indigo"><b> 
16, [?] , 4 

let the missing term be x:

{{{a[1] = 16}}}, {{{a[2]=x}}}, {{{a[3]=4}}}

Now use the fact that in a geometric sequence,

{{{a[2]/a[1]=a[3]/a[2]}}}

{{{x/16 = 4/x}}}

Cross multiply:

{{{x^2=64}}}

{{{sqrt(x^2)=" "+-sqrt(64)}}}

x = ±8

So that one has two possible answers, +8 and -8.

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25, [?] , 225

let the missing term be x:

{{{a[1] = 25}}}, {{{a[2]=x}}}, {{{a[3]=225}}}

Now use the fact that in a geometric sequence,

{{{a[2]/a[1]=a[3]/a[2]}}}

{{{x/25 = 225/x}}}

Cross multiply:

{{{x^2=5625}}}

{{{sqrt(x^2)=" "+-sqrt(5625)}}}

x = ±75

So that one has two possible answers, +75 and -75. 

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2, [?] , 50 

let the missing term be x:

{{{a[1] = 2}}}, {{{a[2]=x}}}, {{{a[3]=50}}}

Now use the fact that in a geometric sequence,

{{{a[2]/a[1]=a[3]/a[2]}}}

{{{x/2 = 50/x}}}

Cross multiply:

{{{x^2=100}}}

{{{sqrt(x^2)=" "+-sqrt(100)}}}

x = ±10

So that one has two possible answers, +10 and -10. 

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1, [?] , 49 

let the missing term be x:

{{{a[1] = 1}}}, {{{a[2]=x}}}, {{{a[3]=49}}}

Now use the fact that in a geometric sequence,

{{{a[2]/a[1]=a[3]/a[2]}}}

{{{x/1 = 49/x}}}

Cross multiply:

{{{x^2=49}}}

{{{sqrt(x^2)=" "+-sqrt(49)}}}

x = ±7

So that one has two possible answers, +7 and -7. 

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3/4, [?] , 3 

let the missing term be x:

{{{a[1] = 3/4}}}, {{{a[2]=x}}}, {{{a[3]=3}}}

Now use the fact that in a geometric sequence,

{{{a[2]/a[1]=a[3]/a[2]}}}

{{{x/(3/4) = 3/x}}}

Cross multiply:

{{{x^2=(3/4)(3)}}}

{{{x^2=9/4}}}

{{{sqrt(x^2)=" "+-sqrt(9/4)}}}

x = ±{{{3/2}}}

So that one has two possible answers, +{{{3/2}}} and {{{-3/2}}}. 

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36, [?] , 4

let the missing term be x:

{{{a[1] = 36}}}, {{{a[2]=x}}}, {{{a[3]=4}}}

Now use the fact that in a geometric sequence,

{{{a[2]/a[1]=a[3]/a[2]}}}

{{{x/36 = 4/x}}}

Cross multiply:

{{{x^2=144}}}

{{{sqrt(x^2)=" "+-sqrt(144)}}}

x = ±12

So that one has two possible answers, +12 and -12.

Edwin</pre>