Question

If the second term of a G.P. is 9 and sum of the infinite numbers is 40.5, then what will be the 3rd term?
Given that the first term is greater then 14.

Answer 1

3

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nth term = a * r ^ (n-1)
=> For 2nd term => 9 = a*r^(2-1) => 9 = ar => r = 9/a
Sum of infinite terms in G.P = a/(1-r) ---> 40.5 = a/(1-r) => 40.5 - 40.5r = a => 40.5 = a + 40.5*9/a => 81a = 2a^2 + 729 => a = 27 or 13.5
As the first term is greater than 14, 13.5 is excluded
So r = 9/27 = 1/3
3rd term is equal to 27*(1/3)^(3-1) = 27*(1/3)^2 = 27/9 = 3