Question

FInd the missing term in the following geometric sequence. 4, __, 500

Answer 1

The answer is 4, 20,100, 500

Answer 2

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

$\dfrac{b}{4}=\dfrac{500}{b}=r\\\\\\\Rightarrow \dfrac{b}{4}=\dfrac{500}{b}\\\\\Rightarrow b^2=4\times500\\\\\Rightarrow b^2=2000\\\\\Rightarrow b=\pm\sqrt{2000}\\\\\Rightarrow b=\pm20\sqrt{5}.$

Thus, the missing term in the given geometric sequence is 20√5  or  -20√5.