Use backtracking to come up with a formula only number 14 bn

Use backtracking to come up with a formula only number 14 b_n = 5 b_n - 1 + 3, b_1 = 3 c_n = c_n - 1 + n, c_1 = 4

Solution

C_n = C_n-1 + n

C_n = C_n-2 + 2n

C_n = C_n-3 + 3n and so on.

therefore

C_n = C₁ + n(n-1)

C₁ = 4 ( initial condition )

Hence C_n = 4 + n(n-1)