The 5th terms of the sequence defined by `t_(1)=2,t_(2)=3 and t_(n)=t_(n-1)+t_(n-2)` for `nge3`

Options

A. 13
B. 15
C. 16
D. 18

Answer

To find the 5th term of the sequence defined by \( t_1 = 2 \), \( t_2 = 3 \), and \( t_n = t_{n-1} + t_{n-2} \) for \( n \geq 3 \), we will follow these steps:

### Step 1: Identify the first two terms
We have:
- \( t_1 = 2 \)
- \( t_2 = 3 \)

### Step 2: Calculate the 3rd term \( t_3 \)
Using the formula \( t_n = t_{n-1} + t_{n-2} \):
\[ t_3 = t_2 + t_1 = 3 + 2 = 5 \]

### Step 3: Calculate the 4th term \( t_4 \)
Now we can find \( t_4 \):
\[ t_4 = t_3 + t_2 = 5 + 3 = 8 \]

### Step 4: Calculate the 5th term \( t_5 \)
Finally, we calculate \( t_5 \):
\[ t_5 = t_4 + t_3 = 8 + 5 = 13 \]

### Conclusion
The 5th term of the sequence is \( t_5 = 13 \).

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