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