Question

Every number of an infinite geometric progression of positive terms is equal to n times the sum of the numbers that follow it. What is the common ratio of progression?
1. 1/(n + 1)
2. 1/(n + 2)
3. 1/(n + 3)
4. 1/(n + 4)

Answer 1

Correct Answer - Option 1 : 1/(n + 1)

Calculation:

Let the geometric progression be a, ar, ar², ....

⇒ a = n × (ar + ar² + ......) 

⇒ ar + ar² + ........ = ar/1- r      (a = n × (ar/1 - r)

⇒ nr = 1 - r

⇒ r = 1/(n + 1)

∴ The required result will be 1/(n + 1).