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The fifth term of the sequence for which...

The fifth term of the sequence for which `t_1= 1, t_2 = 2 and t_(n + 2) = t_n + t_(n + 1)` is

A

5

B

10

C

6

D

8

Text Solution

AI Generated Solution

The correct Answer is:
To find the fifth term of the sequence defined by the recurrence relation \( t_{n+2} = t_n + t_{n+1} \) with initial conditions \( t_1 = 1 \) and \( t_2 = 2 \), we can follow these steps: ### Step-by-Step Solution: 1. **Identify the initial terms**: - We know that \( t_1 = 1 \) and \( t_2 = 2 \). 2. **Calculate the third term \( t_3 \)**: - Using the recurrence relation, we set \( n = 1 \): \[ t_3 = t_1 + t_2 = 1 + 2 = 3 \] 3. **Calculate the fourth term \( t_4 \)**: - Now, set \( n = 2 \): \[ t_4 = t_2 + t_3 = 2 + 3 = 5 \] 4. **Calculate the fifth term \( t_5 \)**: - Next, set \( n = 3 \): \[ t_5 = t_3 + t_4 = 3 + 5 = 8 \] 5. **Conclusion**: - The fifth term of the sequence is \( t_5 = 8 \). ### Final Answer: The fifth term of the sequence is **8**.
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