Which sequence is generated by the function f(n + 1) = f(n) - 2 for f(1) = 10?
-10, -12, -14, -16, -18, …
-2, 8, 18, 28, 38, …
8, 18, 28, 38, 48, …
10, 8, 6, 4, 2, …

Solution:

Given f(n + 1) = f(n) - 2 and f(1) = 10

Let us take some values as natural numbers for n

n = 1, 2, 3, 4……….

When n = 1; f(1 + 1) = f(1) - 2 ⇒ f(2) = 10 -2 = 8 ; f(2) = 8

When n = 2; f(2 + 1) = f(2) - 2 ⇒ f(3) = 8 - 2 = 6; f(2) = 6

When n = 3; f(3 + 1) = f(3) - 2 ⇒ f(4) = 6 - 2 = 4; f(3) = 4

When n = 4; f(4 + 1) = f(4) - 2 ⇒ f(5) = 4 - 2 = 2; f(4) = 2

The sequence is 10, 8, 6, 4, 2…

Which sequence is generated by the function f(n + 1) = f(n) - 2 for f(1) = 10?

Summary:

The sequence is generated by the function f(n + 1) = f(n) - 2 for f(1) = 10 is 10, 8, 6, 4, 2…