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.

Answer :

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


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