The first three terms of a sequence are `3, 3, 6` and each term after the sum of two terms preceding it, then the `8th` term of the sequence

Options

A. 15
B. 24
C. 39
D. 63

Answer

To find the 8th term of the sequence given the first three terms as 3, 3, and 6, and knowing that each subsequent term is the sum of the two preceding terms, we can follow these steps:

### Step 1: Identify the first three terms
The first three terms of the sequence are:
- \( a_1 = 3 \)
- \( a_2 = 3 \)
- \( a_3 = 6 \)

### Step 2: Write the formula for subsequent terms
Each term after the third term is defined as:
- \( a_n = a_{n-1} + a_{n-2} \) for \( n \geq 4 \)

### Step 3: Calculate the next terms
Now, we will calculate the next terms up to the 8th term.

- **4th term**:
\[ a_4 = a_3 + a_2 = 6 + 3 = 9 \]

- **5th term**:
\[ a_5 = a_4 + a_3 = 9 + 6 = 15 \]

- **6th term**:
\[ a_6 = a_5 + a_4 = 15 + 9 = 24 \]

- **7th term**:
\[ a_7 = a_6 + a_5 = 24 + 15 = 39 \]

- **8th term**:
\[ a_8 = a_7 + a_6 = 39 + 24 = 63 \]

### Conclusion
Thus, the 8th term of the sequence is \( 63 \).

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