Question

Find the b3, b4, and b5 terms of the sequence: b_(n)=100b_(n-2)+(b_(n-1))^(2), b_(1)=2, b_(2)=5

Answer 1

`b_(n)=100b_(n-2)+b_(n-1)^2 \\ b_(1)=2 \\ b_(2)=5`


`b_(3)=100b_(3-2)+b_(3-1)^2 \\ b_(3)=100b_(1)+b_(2)^2 \\ b_(3)=100(2)+5^(2) \\ b_(3)=200+25 \\ b_(3)=225`


`b_(4)=100b_(4-2)+b_(4-1)^(2) \\ b_(4)=100b_(2)+b_(3)^(2) \\ b_(4)=100(5)+225^(2) \\ b_(4)=500+50625 \\ b_(4)=51125`


`b_(5)=100b_(5-2)+b_(5-1)^(2) \\ b_(5)=100b_(3)+b_(4)^(2) \\ b_(5)=100(225)+51125^(2) \\ b_(5)=22500+2613765625 \\ b_(5)=2613788125`

[tex]b_{3}=225[tex]
[tex]b_{4}=51125[tex]
[tex]b_{5}=2613788125[tex]