Question

Type your response in the box. Here is a function that describes a sequence called the Lucas numbers, which is similar to the Fibonacci sequence: f(n) = fin - 1) + fin - 2); f(1) = 2; f(2)= 1.

Regarding the Lucas numbers sequence, which is similar to the Fibonacci sequence:

A) The relationship between terms involves adding the two preceding terms.
B) The relationship between terms involves multiplying the two preceding terms.
C) The first six terms of the sequence are 2, 1, 3, 4, 7, 11.
D) The 12th term of the sequence is 90.

Answer 1

The Lucas numbers sequence, similar to the Fibonacci sequence, has a relationship between terms that involves adding the two preceding terms. The first six terms of the sequence are 2, 1, 3, 4, 7, 11. The 12th term of the sequence is 199.

Step-by-step explanation:

The Lucas numbers sequence, similar to the Fibonacci sequence, has a relationship between terms that involves adding the two preceding terms. This is option A.

The first six terms of the sequence are 2, 1, 3, 4, 7, 11. So, option C is correct.

To find the 12th term of the sequence, we can use the recursive formula given: f(n) = f(n-1) + f(n-2). Starting with f(1) = 2 and f(2) = 1, we can calculate f(12) step by step:

• f(3) = f(2) + f(1) = 1 + 2 = 3
• f(4) = f(3) + f(2) = 3 + 1 = 4
• f(5) = f(4) + f(3) = 4 + 3 = 7
• f(6) = f(5) + f(4) = 7 + 4 = 11
• f(7) = f(6) + f(5) = 11 + 7 = 18
• f(8) = f(7) + f(6) = 18 + 11 = 29
• f(9) = f(8) + f(7) = 29 + 18 = 47
• f(10) = f(9) + f(8) = 47 + 29 = 76
• f(11) = f(10) + f(9) = 76 + 47 = 123
• f(12) = f(11) + f(10) = 123 + 76 = 199

Therefore, the 12th term of the Lucas numbers sequence is 199, which differs from option D.