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

`(b)/(4)=(500)/(b)=r\\\\\\\Rightarrow (b)/(4)=(500)/(b)\\\\\Rightarrow b^2=4*500\\\\\Rightarrow b^2=2000\\\\\Rightarrow b=\pm√(2000)\\\\\Rightarrow b=\pm20√(5).`

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