Question

Solve recurrence relation using substitution method.

T(1) = 1

T(n) = T(n-1) + n + 18

Answer 1

To solve the given recurrence relation using the substitution method, plug in values and observe patterns to find a general formula. The general formula for T(n) is 20n for all n >= 1.

Step-by-step explanation:

To solve the given recurrence relation using the substitution method, we can plug in values and observe patterns to find a general formula.

Step 1: Substitute n = 1 into the equation to find T₁: T(1) = T(1-1) + 1 + 18 = T(0) + 1 + 18 = 1 + 1 + 18 = 20.

Step 2: Use the general form T₂ = T(2-1) + 2 + 18 = T₁ + 2 + 18 = 20 + 2 + 18 = 40. By observing the pattern, we can deduce that T(n) = 20n for all n >= 1.