Question

If f, left bracket, 1, right bracket, equals, 9 f ( 1 ) = 9 f(1)=9 and f, left bracket, n, right bracket, equals, f, left bracket, n, minus, 1, right bracket, plus, 5 f ( n ) = f ( n − 1 ) 5 f(n)=f(n−1) 5 then find the value of f, left bracket, 6, right bracket f ( 6 ) f(6).

Answer 1

To find the value of f(6), we can use the recursive definition given in the question: f(1) = 9 and f(n) = f(n-1) + 5. By using this definition, we can calculate the values of f(2), f(3), f(4), f(5), and finally f(6), which is 34.

Step-by-step explanation:

To find the value of f(6), we can use the recursive definition given in the question:
f(1) = 9
f(n) = f(n-1) + 5

We can use this definition to find the values of f(2), f(3), f(4), f(5), and finally f(6). Starting with f(1) = 9, we can calculate:
f(2) = f(1) + 5 = 9 + 5 = 14
f(3) = f(2) + 5 = 14 + 5 = 19
f(4) = f(3) + 5 = 19 + 5 = 24
f(5) = f(4) + 5 = 24 + 5 = 29
f(6) = f(5) + 5 = 29 + 5 = 34

Therefore, the value of f(6) is 34.

Answer 2

To find the value of f(6), you can use the given recursive formula and substitute the values to find the sequence. By substituting the values step by step, you can find that f(6) is equal to 34.

Step-by-step explanation:

To find the value of f(6), we can use the given recursive formula. We know that f(1) = 9. Substituting this into the formula, we have f(n) = f(n-1) + 5. Using this formula, we can find the values of f(2), f(3), f(4), f(5), and finally f(6).

f(2) = f(1) + 5 = 9 + 5 = 14

1. f(3) = f(2) + 5 = 14 + 5 = 19
2. f(4) = f(3) + 5 = 19 + 5 = 24
3. f(5) = f(4) + 5 = 24 + 5 = 29
4. f(6) = f(5) + 5 = 29 + 5 = 34

Therefore, f(6) = 34.