(b) \( 4 ; 11 ; 18,25 \ldots \) is a given sequence: (1) Determine the \( 45^{\circ} \) term. (2) Which term of the sequence is 627?

To solve the given sequence \( 4 ; 11 ; 18,25 \ldots \), we need to first find a pattern. Looking at the differences between terms: - \( 11 - 4 = 7 \) - \( 18 - 11 = 7 \) - \( 25 - 18 = 7 \) This shows that each term increases by 7. The sequence can be represented by the formula: \( a_n = 4 + 7(n - 1) \) or simplified: \( a_n = 7n - 3 \). (1) To find the \( 45^{th} \) term: \( a_{45} = 7(45) - 3 = 315 - 3 = 312 \). (2) To determine which term is 627, we set the \( n \)th term equal to 627: \( 7n - 3 = 627 \) \( 7n = 630 \) \( n = 90 \). Thus, \( 627 \) is the \( 90^{th} \) term of the sequence.