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 Solution For geometric progression f( 1 ) = 2 , f( 4 ) = 54 , then find n such that f(n) = 18 .Solution:Your problem -> For geometric progression f( 1 ) = 2 , f( 4 ) = 54 , then find n such that f(n) = 18 .We know that, a_n = a × r^(n-1)Here a_1 = 2=> a × r^(1 - 1) = 2=> a × r^0 = 2=> a = 2 ->(1)a_4 = 54=> a × r^(4 - 1) = 54=> a × r^3 = 54 ->(2)Solving (1) and (2), we get a = 2 and r = 3Let n be the term such that f(n) = 18We know that, a_n = a × r^(n-1)=> 2 × 3^(n-1) = 18=> 3^(n-1) = 9=> 3^(n-1) = 3^2=> n - 1 = 2=> n = 2 + 1=> n = 3 Solution provided by AtoZmath.com Any wrong solution, solution improvement, feedback then Submit Here Want to know about AtoZmath.com and me