What is a possible value for the missing term of the geometric sequence 1250 , __ , 50 ,..?

Solution:

Given that the sequence is 1250 , __ , 50 ,..., which is a geometric sequence.

Let the missing number be ‘x’

A GP is given as a, ar, ar² , ar³ .......arⁿ

Since the given equation is in the GP, we know that the common ratio is  ar/a = ar²/ar

∴ x/1250 = 50/x

x² = 1250 × 50

x² = 62500

x = 250

What is a possible value for the missing term of the geometric sequence 1250 , __ , 50,..?

Summary:

The possible value for the missing term of the geometric sequence 1250,__,50,... is 250.