A sequence is defined by the recursive formula f(n+) = f(n) -2. If f(1) =18 what is f(5)?

Work Shown:

Plug in n = 1 to find the next term

f(n+1) = f(n) - 2

f(1+1) = f(1) - 2 ... replace every n with 1

f(2) = f(1) - 2

f(2) = 18-2 replace f(1) with 18

f(2) = 16

We'll use this to get the next term. Plug in n = 2

f(n+1) = f(n) - 2

f(2+1) = f(2) - 2 ... replace every n with 2

f(3) = f(2) - 2

f(3) = 16 - 2 ... replace f(2) with 16

f(3) = 14

This process keeps going until we reach f(5)

Plug in n = 3

f(n+1) = f(n) - 2

f(3+1) = f(3) - 2

f(4) = f(3) - 2

f(4) = 14-2

f(4) = 12

and finally plug in n = 4

f(n+1) = f(n) - 2

f(4+1) = f(4) - 2

f(5) = f(4) - 2

f(5) = 12 - 2

f(5) = 10

The summary is basically we subtract 2 from each term to get the next term. The sequence is 18, 16, 14, 12, 10 which is arithmetic.

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