Question

A sequence is defined by f(0) = -3, f(n) = f(n-1) + 0.5 for n ≥ 1.

1.
Write the first five terms of this sequence, starting with term 0.
2.
Write the nth term definition of this sequence.

Answer 1

1.

f(0) = -3

f(1) = f(0) + 0.5 = -3 + 0.5 = -2.5

f(2) = f(1) + 0.5 = -2.5 + 0.5 = -2

f(3) = f(2) + 0.5 = -2 + 0.5 = -1.5

f(4) = f(3) + 0.5 = -1.5 + 0.5 = -1

2.

f(n) = 0.5n - 3

This function is linear.