3. Consider the arithmetic sequence: \( -8 ;-2 ; 4 ; 10 ; \ldots \) 3.1 Write down the next term of the sequence 3.2 If the nth term of the sequence is 148 , determine the value of \( n \)

Let's analyze the given arithmetic sequence and solve the problems step by step. **Given Sequence:** \(-8, -2, 4, 10, \ldots\) ### 3.1. Write Down the Next Term of the Sequence In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. - **First Term (\(a_1\))**: \(-8\) - **Common Difference (\(d\))**: \(-2 - (-8) = 6\) To find the next term after \(10\): \[ \text{Next Term} = 10 + d = 10 + 6 = 16 \] **Answer:** The next term is **16**. --- ### 3.2. Determine the Value of \(n\) When the \(n^{th}\) Term is 148 The formula for the \(n^{th}\) term (\(a_n\)) of an arithmetic sequence is: \[ a_n = a_1 + (n - 1) \cdot d \] Given: - \(a_n = 148\) - \(a_1 = -8\) - \(d = 6\) Plugging in the values: \[ 148 = -8 + (n - 1) \cdot 6 \] \[ 148 + 8 = 6(n - 1) \] \[ 156 = 6(n - 1) \] \[ \frac{156}{6} = n - 1 \] \[ 26 = n - 1 \] \[ n = 27 \] **Answer:** The value of \(n\) is **27**.