Q. 5

# There is n arithmetic means between 9 and 27. If the ratio of the last mean to the first mean is 2 : 1, find the value of n.

To find: The value of n

Given: (i) The numbers are 9 and 27

(ii) The ratio of the last mean to the first mean is 2 : 1

Formula used: (i) , where, d is the common difference

n is the number of arithmetic means

(ii) An = a + nd

We have 9 and 27,

Using Formula,   Using Formula, An = a + nd

First mean i.e.,    … (i)

Last mean i.e.,   An … (ii)

The ratio of the last mean to the first mean is 2 : 1 Substituting the value of A1 and An from eqn. (i) and (ii)  27n + 9 = 18n + 54

9n = 45

n = 5

Ans) The value of n is 5

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Geometric Progression58 mins  General Term of Miscellaneous progression46 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 