Each term of a sequence is the sum of its preceding two terms from the third term onwards. The second term of the sequence is -1 and the 10th term is 29. The first term is `"_________"`

Answer

To find the first term of the sequence, we will denote the terms of the sequence as \( a_1, a_2, a_3, \ldots \) and apply the information given in the problem.

### Step-by-Step Solution:

1. **Understanding the Sequence**:
The sequence is defined such that each term from the third term onward is the sum of the two preceding terms. This can be expressed as:
\[ a_{k+2} = a_k + a_{k+1} \]
for \( k \geq 1 \).

2. **Given Values**:
We are given:
- \( a_2 = -1 \)
- \( a_{10} = 29 \)

3. **Expressing Terms**:
We can express the terms in terms of \( a_1 \):
- For \( a_3 \):
\[ a_3 = a_1 + a_2 = a_1 - 1 \]
- For \( a_4 \):
\[ a_4 = a_2 + a_3 = -1 + (a_1 - 1) = a_1 - 2 \]
- For \( a_5 \):
\[ a_5 = a_3 + a_4 = (a_1 - 1) + (a_1 - 2) = 2a_1 - 3 \]
- For \( a_6 \):
\[ a_6 = a_4 + a_5 = (a_1 - 2) + (2a_1 - 3) = 3a_1 - 5 \]
- For \( a_7 \):
\[ a_7 = a_5 + a_6 = (2a_1 - 3) + (3a_1 - 5) = 5a_1 - 8 \]
- For \( a_8 \):
\[ a_8 = a_6 + a_7 = (3a_1 - 5) + (5a_1 - 8) = 8a_1 - 13 \]
- For \( a_9 \):
\[ a_9 = a_7 + a_8 = (5a_1 - 8) + (8a_1 - 13) = 13a_1 - 21 \]
- For \( a_{10} \):
\[ a_{10} = a_8 + a_9 = (8a_1 - 13) + (13a_1 - 21) = 21a_1 - 34 \]

4. **Setting Up the Equation**:
We know that \( a_{10} = 29 \), so we can set up the equation:
\[ 21a_1 - 34 = 29 \]

5. **Solving for \( a_1 \)**:
Rearranging the equation gives:
\[ 21a_1 = 29 + 34 \]
\[ 21a_1 = 63 \]
\[ a_1 = \frac{63}{21} = 3 \]

### Conclusion:
The first term \( a_1 \) is \( 3 \).