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