a) The sequence of page numbers is: 3, 7, 11, 15, 19.
To describe the rule for the sequence, we can observe that each term increases by a constant amount from the previous term. Specifically:
- From 3 to 7, the increase is 4 (7 - 3 = 4)
- From 7 to 11, the increase is also 4 (11 - 7 = 4)
- From 11 to 15, the increase is again 4 (15 - 11 = 4)
- From 15 to 19, the increase is again 4 (19 - 15 = 4)
Thus, the common difference of the sequence is 4.
In general, we can describe the \( n^{th} \) term of the sequence as: \[ a_n = 3 + (n - 1) \cdot 4 \]
b) To find the next two terms in the sequence after 19, we can add the common difference (4) to the last term:
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The next term after 19: \[ 19 + 4 = 23 \]
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The term after that: \[ 23 + 4 = 27 \]
Thus, the next two terms of the sequence are 23 and 27.
In summary:
- The common difference is \( 4 \).
- The next two terms are \( 23 \) and \( 27 \).