Six examples of Fibonacci-type sequences asking students to find the three missing terms in each pattern.

To solve the problem, we need to identify the pattern in each sequence and use it to find the missing terms. Let's go through each sequence step by step.

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Sequence (a): \( 1, 1, 2, 3, 5, 8, \_, \_, \_ \)

This is a classic Fibonacci sequence, where each term is the sum of the two preceding terms:
\[
a_n = a_{n-1} + a_{n-2}
\]

- The next term after 8 is \( 5 + 8 = 13 \).
- The next term after 13 is \( 8 + 13 = 21 \).
- The next term after 21 is \( 13 + 21 = 34 \).

Thus, the missing terms are:
\[
13, 21, 34
\]

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Sequence (b): \( 6, 9, 15, 24, \_, \_, \_ \)

Here, each term is the sum of the two preceding terms:
\[
a_n = a_{n-1} + a_{n-2}
\]

- The next term after 24 is \( 15 + 24 = 39 \).
- The next term after 39 is \( 24 + 39 = 63 \).
- The next term after 63 is \( 39 + 63 = 102 \).

Thus, the missing terms are:
\[
39, 63, 102
\]

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Sequence (c): \( \_, \_, \_, 12, 19, 31, \ldots \)

Again, this is a Fibonacci-type sequence where each term is the sum of the two preceding terms:
\[
a_n = a_{n-1} + a_{n-2}
\]

We work backward to find the missing terms:
- The term before 19 is \( 31 - 19 = 12 \).
- The term before 12 is \( 19 - 12 = 7 \).
- The term before 7 is \( 12 - 7 = 5 \).

Thus, the missing terms are:
\[
5, 7, 12
\]

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Sequence (d): \( 0.5, 1, 1.5, \_, 4, \_, \_ \)

This is also a Fibonacci-type sequence where each term is the sum of the two preceding terms:
\[
a_n = a_{n-1} + a_{n-2}
\]

- The next term after 1.5 is \( 1 + 1.5 = 2.5 \).
- The next term after 2.5 is \( 1.5 + 2.5 = 4 \) (which is already given).
- The next term after 4 is \( 2.5 + 4 = 6.5 \).
- The next term after 6.5 is \( 4 + 6.5 = 10.5 \).

Thus, the missing terms are:
\[
2.5, 6.5, 10.5
\]

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Sequence (e): \( 1, -1, 0, \_, -1, \_, \_ \)

This is a Fibonacci-type sequence where each term is the sum of the two preceding terms:
\[
a_n = a_{n-1} + a_{n-2}
\]

- The next term after 0 is \( -1 + 0 = -1 \).
- The next term after -1 is \( 0 + (-1) = -1 \).
- The next term after -1 is \( -1 + (-1) = -2 \).

Thus, the missing terms are:
\[
-1, -1, -2
\]

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Sequence (f): \( a, b, \_, \_, \_ \)

This is a Fibonacci-type sequence where each term is the sum of the two preceding terms:
\[
a_n = a_{n-1} + a_{n-2}
\]

- The next term after \( b \) is \( a + b \).
- The next term after \( a + b \) is \( b + (a + b) = a + 2b \).
- The next term after \( a + 2b \) is \( (a + b) + (a + 2b) = 2a + 3b \).

Thus, the missing terms are:
\[
a + b, a + 2b, 2a + 3b
\]

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Final Answers:

\[
\boxed{
\begin{array}{ll}
(a) & 13, 21, 34 \\
(b) & 39, 63, 102 \\
(c) & 5, 7, 12 \\
(d) & 2.5, 6.5, 10.5 \\
(e) & -1, -1, -2 \\
(f) & a + b, a + 2b, 2a + 3b \\
\end{array}
}
\]