Question

Calculate the nth term of a recursive sequence given the equation.

a) aₙ = f(aₙ₋₁)
b) aₙ = f(n, aₙ₋₁)
c) aₙ = f(n)
d) aₙ = f(aₙ₊₁)

Answer 1

A recursive sequence can be defined using different equations depending on the given information.

Step-by-step explanation:

A recursive sequence is a sequence of numbers where each term is defined in terms of one or more previous terms. The nth term of a recursive sequence can be calculated using different equations depending on the given information:

a) aₙ = f(aₙ₋₁): In this equation, the nth term depends on the value of the (n-1)th term.

b) aₙ = f(n, aₙ₋₁): In this equation, the nth term depends on both the value of n and the (n-1)th term.

c) aₙ = f(n): In this equation, the nth term depends only on the value of n.

d) aₙ = f(aₙ₊₁): In this equation, the nth term depends on the value of the (n+1)th term.