Question

Eric considers a sequence of numbers given by the following definition

f(1) = 7 and f(n)=f(n-1) + 4
the first 4 numbers are: 4, 11, 18, 25
What is Eric's mistake here?

Answer 1

Eric's mistake is in the initial values of the sequence. According to the definition, f(1) = 7, but the given sequence starts with 4. The correct sequence starting from f(1) = 7 is 7, 11, 15, 19, 23.

Step-by-step explanation:

Eric's mistake lies in the initial values of the sequence. According to the definition given, f(1) = 7. However, the first number in the given sequence is 4, which is incorrect. This mistake affects all subsequent numbers in the sequence as well.

To find the correct values of the sequence, we can start from f(1) = 7 and use the recursive formula f(n) = f(n-1) + 4. Using this formula, we can calculate the correct sequence as follows:

1. f(1) = 7
2. f(2) = f(1) + 4 = 7 + 4 = 11
3. f(3) = f(2) + 4 = 11 + 4 = 15
4. f(4) = f(3) + 4 = 15 + 4 = 19
5. f(5) = f(4) + 4 = 19 + 4 = 23

Therefore, the correct sequence starting from f(1) = 7 is: 7, 11, 15, 19, 23.