Practice your arithmetic skills with this Alpha Exercise worksheet featuring six Fibonacci-style number patterns.

To solve the problem of finding the missing terms in these Fibonacci-type sequences, we need to identify the pattern in each sequence. Let's analyze each sequence step by step.

(a) Sequence: \(2, 2, 4, 6, 10, \_, \_, \_\)

- The sequence starts with \(2, 2\).
- The next term is \(4 = 2 + 2\).
- The next term is \(6 = 2 + 4\).
- The next term is \(10 = 4 + 6\).

The pattern is that each term is the sum of the two preceding terms. Therefore:
- The next term is \(6 + 10 = 16\).
- The next term is \(10 + 16 = 26\).
- The next term is \(16 + 26 = 42\).

So, the sequence is: \(2, 2, 4, 6, 10, 16, 26, 42, \ldots\).

(b) Sequence: \(7, 1, 8, 9, \_, \_, \_\)

- The sequence starts with \(7, 1\).
- The next term is \(8 = 7 + 1\).
- The next term is \(9 = 1 + 8\).

The pattern is that each term is the sum of the two preceding terms. Therefore:
- The next term is \(8 + 9 = 17\).
- The next term is \(9 + 17 = 26\).
- The next term is \(17 + 26 = 43\).

So, the sequence is: \(7, 1, 8, 9, 17, 26, 43, \ldots\).

(c) Sequence: \(4, 5, 9, 14, \_, \_, \_\)

- The sequence starts with \(4, 5\).
- The next term is \(9 = 4 + 5\).
- The next term is \(14 = 5 + 9\).

The pattern is that each term is the sum of the two preceding terms. Therefore:
- The next term is \(9 + 14 = 23\).
- The next term is \(14 + 23 = 37\).
- The next term is \(23 + 37 = 60\).

So, the sequence is: \(4, 5, 9, 14, 23, 37, 60, \ldots\).

(d) Sequence: \(10, 12, 22, 34, \_, \_, \_\)

- The sequence starts with \(10, 12\).
- The next term is \(22 = 10 + 12\).
- The next term is \(34 = 12 + 22\).

The pattern is that each term is the sum of the two preceding terms. Therefore:
- The next term is \(22 + 34 = 56\).
- The next term is \(34 + 56 = 90\).
- The next term is \(56 + 90 = 146\).

So, the sequence is: \(10, 12, 22, 34, 56, 90, 146, \ldots\).

(e) Sequence: \(16, 14, 30, 44, \_, \_, \_\)

- The sequence starts with \(16, 14\).
- The next term is \(30 = 16 + 14\).
- The next term is \(44 = 14 + 30\).

The pattern is that each term is the sum of the two preceding terms. Therefore:
- The next term is \(30 + 44 = 74\).
- The next term is \(44 + 74 = 118\).
- The next term is \(74 + 118 = 192\).

So, the sequence is: \(16, 14, 30, 44, 74, 118, 192, \ldots\).

(f) Sequence: \(100, 200, 300, 500, \_, \_, \_\)

- The sequence starts with \(100, 200\).
- The next term is \(300 = 100 + 200\).
- The next term is \(500 = 200 + 300\).

The pattern is that each term is the sum of the two preceding terms. Therefore:
- The next term is \(300 + 500 = 800\).
- The next term is \(500 + 800 = 1300\).
- The next term is \(800 + 1300 = 2100\).

So, the sequence is: \(100, 200, 300, 500, 800, 1300, 2100, \ldots\).

Final Answer:

\[
\boxed{
\begin{array}{l}
(a) \ 16, 26, 42 \\
(b) \ 17, 26, 43 \\
(c) \ 23, 37, 60 \\
(d) \ 56, 90, 146 \\
(e) \ 74, 118, 192 \\
(f) \ 800, 1300, 2100 \\
\end{array}
}
\]