Question

A sequence is defined as follows: \( a_1 = 1, a_2 = 2 \), and \( a_n = a_{n-1} + a_{n-2} \) for \( n \geq 3 \). What is the 6th term of the sequence?

• A. 5
• B. 8
• C. 13
• D. 21

Hint:

For recursive sequences, compute each term iteratively using the given relation and initial conditions. Double-check the term number.

Answer 1

The Correct Option is C

Step 1: Identify the sequence by computing the terms step-by-step using the given recurrence relation \( a_n = a_{n-1} + a_{n-2} \) with initial terms \( a_1 = 1 \) and \( a_2 = 2 \).
Step 2: Calculate the terms:
- \( a_3 = a_2 + a_1 = 2 + 1 = 3 \),
- \( a_4 = a_3 + a_2 = 3 + 2 = 5 \),
- \( a_5 = a_4 + a_3 = 5 + 3 = 8 \),
- \( a_6 = a_5 + a_4 = 8 + 5 = 13 \).
Step 3: Identify the 6th term. The 6th term is \( a_6 = 13 \).
Step 4: Verify the sequence.
The sequence is 1, 2, 3, 5, 8, 13, which matches the Fibonacci-like pattern, confirming the calculation.