Question

A sequence of numbers is defined recursively as follows: (a(1) = -6) and (a(n) = a(n - 1) + 2). Which equation represents the same sequence of numbers?

a) (f(n) = -8n + 2)

b) (f(n) = -8 + 2n)

c) (f(n) = n + 2)

d) (f(n) = -6n)

Answer 1

The equation that represents the sequence is f(n) = -6 + 2(n-1)

Step-by-step explanation:

The sequence of numbers is defined recursively as follows:

1. a(1) = -6
2. a(n) = a(n - 1) + 2

To find the equation that represents the same sequence of numbers, we need to simplify the recursive definition. By observing the pattern, we can see that each term is obtained by adding 2 to the previous term. So, the equation that represents the sequence is f(n) = -6 + 2(n-1).

Therefore, the correct equation that represents the same sequence of numbers is (f(n) = -6 + 2(n-1)).