Q5 of 167 Page 19

There are n A.M.s between 3 and 17. The ratio of the last mean to the first mean is 3 : 1. Find the value of n.

Let the series be 3, A1, A2, A3, ........, An, 17


From the data,


We know total terms in AP are n + 2


So 17 is the (n + 2)th term


We know,


An = a + (n - 1)d


So, 17 = 3 + (n + 2 - 1)d



Therefore,



And



Since,




9n + 51 = 17n + 3


8n = 48



n = 6


There are 6 terms in AP


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