How do I determine the constant difference(d)? \[ d=T_{2}-T_{1}=T_{3}-T_{2} \] Example: Given: \( \quad 3 ; 5 ; 7 ; 9 ; \ldots \ldots ; n \) \[ \begin{array}{l} T_{1}(\mathrm{a})=\text { First Term }=3 \\ \boldsymbol{T}_{2}=\text { Second Term = } 5 \\ \boldsymbol{T}_{3} \text { = Fourth Term = } 7 \\ d=5-3=7-5 \\ 2=2 \\ d=2 \end{array} \]

To determine the constant difference \( d \) in an arithmetic sequence, you can follow these steps: 1. **Identify the terms of the sequence**: In your example, the sequence is \( 3, 5, 7, 9, \ldots \). 2. **Label the terms**: - \( T_1 = 3 \) (First Term) - \( T_2 = 5 \) (Second Term) - \( T_3 = 7 \) (Third Term) - \( T_4 = 9 \) (Fourth Term) 3. **Calculate the differences**: - The difference between the second term and the first term is: \[ d = T_2 - T_1 = 5 - 3 = 2 \] - The difference between the third term and the second term is: \[ d = T_3 - T_2 = 7 - 5 = 2 \] - The difference between the fourth term and the third term is: \[ d = T_4 - T_3 = 9 - 7 = 2 \] 4. **Confirm the constant difference**: Since all calculated differences are equal, we can conclude that the constant difference \( d \) is indeed: \[ d = 2 \] Thus, the constant difference \( d \) in the given arithmetic sequence is \( 2 \).