Question

In a sequence, each term after the first is obtained by adding the product of the previous two terms to the previous term. If the first two terms are 1 and 2, what is the fifth term?

• A. 68
• B. 60
• C. 96
• D. 106

Hint:

For recursive sequences, compute each term step-by-step using the given rule, and verify calculations to ensure accuracy.

Answer 1

The Correct Option is B

To solve the problem, we need to find the fifth term of the sequence where each term after the first is obtained by adding the product of the previous two terms to the previous term, starting with 1 and 2.

1. Understanding the Concepts:

- Sequence Definition: Each term \( T_n \) is given by: \[ T_n = T_{n-1} + (T_{n-1} \times T_{n-2}) = T_{n-1} (1 + T_{n-2}) \] - Given: \( T_1 = 1 \), \( T_2 = 2 \)

2. Calculate Terms Step-by-Step:

- \( T_1 = 1 \)
- \( T_2 = 2 \)
- \( T_3 = T_2 + (T_2 \times T_1) = 2 + (2 \times 1) = 4 \)
- \( T_4 = T_3 + (T_3 \times T_2) = 4 + (4 \times 2) = 4 + 8 = 12 \)
- \( T_5 = T_4 + (T_4 \times T_3) = 12 + (12 \times 4) = 12 + 48 = 60 \)

Final Answer:

The fifth term of the sequence is 60.