A sequence is defined by the formula f(n + 1) = f(n) - 3. If f(4) = 22, what is f(1)?

Solution:

Given f(n + 1) = f(n) - 3 and f(4) = 22

Let us find the value of f(1) using the recursive formula:

Since f(4) = 22

Put n = 3;

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

f(4) = f(3) - 3

22 = f(3) - 3

Therefore, f(3) = 25

Put n = 2;

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

f(3) = f(2) - 3

25 = f(2) - 3

Therefore, f(2) = 28

Put n = 1;

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

f(2) = f(1) - 3

28 = f(1) - 3

Therefore, f(1) = 31

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A sequence is defined by the formula f(n + 1) = f(n) - 3. If f(4) = 22, what is f(1)?

Summary:

For the given sequence is defined by the formula f(n + 1) = f(n) - 3 and f(4) = 22, f(1) is 31.