Answer: The missing term in the given geometric sequence is 20√5 or -20√5.
Step-by-step explanation: We are given to find the missing term in the following geometric sequence :
4, ?, 500, . . .
Let b represents the missing term.
Since the given sequence is a geometric one, so there common ratio r such that
[tex]\dfrac{b}{4}=\dfrac{500}{b}=r\\\\\\\Rightarrow \dfrac{b}{4}=\dfrac{500}{b}\\\\\Rightarrow b^2=4\times500\\\\\Rightarrow b^2=2000\\\\\Rightarrow b=\pm\sqrt{2000}\\\\\Rightarrow b=\pm20\sqrt{5}.[/tex]
Thus, the missing term in the given geometric sequence is 20√5 or -20√5.
