Define a sequence (a_ n ) by a₁=5, a_ n =a₁ a₂ a_ n-1 +4 for n>1 . Then _ n a_ n a_ n-1

Step-by-step solution

a₁=5a_ n =a₁ a₂ a_ n-1 +4a₂=a₁+4=9a₃=a₁ a₂+4=5 9+4=49a₄=a₁ a₂ a₃+4=2209a₅=a₁ a₂ a₃ a₄+4=4870849=(2207)²a₅= (a₄-2 )²a₄=(49-2)²= (a₃-2 )²a₃=(9-2)²= (a₂-2 )²a n= (a_ n-1 -2 )² a_ n =a_ n-1 -2 a_ n a_ n-1 = a_ n-1 -2 a_ n-1 =1- _ n 2 a_ n-1 _ n a_ n-1 = =1