Question

The first four terms of a sequence are shown below:

7, 4, 1, −2

Which of the following functions best defines this sequence?

f(1) = 7, f(n + 1) = f(n) + 3; for n ≥ 1
f(1) = 7, f(n + 1) = f(n) − 4; for n ≥ 1
f(1) = 7, f(n + 1) = f(n) + 4; for n ≥ 1
f(1) = 7, f(n + 1) = f(n) − 3; for n ≥ 1

Answer 1

Normally, this is a substitution. Pick n = 1 and see what happens,

f(1 + 1) = f(2) = f(1) + 3 = 7 + 3 = 10
f(1 + 1) = f(2) = f(1) − 4 = 7 - 4 = 3
f(1 + 1) = f(2) = f(1) + 4 = 7 + 4 = 11
f(1 + 1) = f(2) = f(1) − 3 = 7 - 3 = 4

Which, if any, actually reproduced the second value?

Answer 2

D