The first five terms of the recursive sequence are: 4, 20, 100, 500, 2500.
A recursive sequence is a sequence in which the nth terms are defined using one or more previous terms along with an initial condition.
A typical example of a recursive sequence of formula is the Fibonacci sequence.
The given sequence is a recursive sequence because each next term is 5 times the previous term. The first term a₁ is given as 4.
Using the recursive formula aₙ = 5 * a(n-1), we can find the next terms:
a₂ = 5 * a₁ = 5 * 4 = 20
a₃ = 5 * a₂ = 5 * 20 = 100
a₄ = 5 * a₃ = 5 * 100 = 500
a₅ = 5 * a₄ = 5 * 500 = 2500
Thus, the first five terms of the sequence are: 4, 20, 100, 500, 2500.