Answer:
Geometric sequence states that a sequence in which a number that follows the pattern were the next term is found by multiplying the constant common ratio term(r).
For the sequence: [tex]a, ar, ar^2, ar^3,.....[/tex]
The formula for the nth geometric sequence is given by:
[tex]a_n =ar^{n-1}[/tex]
where
a is the first term
r is the common ratio
n is the number of terms.
Given that:
A geometric sequence:
50, _[tex]a_2[/tex]___, 450
Here, a = first term = 50
[tex]a_3 = 450[/tex]
Using the nth geometric sequence formula:
[tex]a_3 = ar^2[/tex]
or
[tex]ar^2 = 450[/tex]
Substitute the value of a , to solve for r;
[tex]50r^2 = 450[/tex]
Divide both sides by 50 we get;
[tex]r^2 = 9[/tex]
[tex]r = \sqrt{9} = 3[/tex]
To find the term [tex]a_2[/tex];
[tex]a_2 = ar[/tex]
Substitute the given values we have;
[tex]a_2 = 50 \cdot 3 = 150[/tex]
Therefore, the possible value for the missing term of the geometric sequence is 150
