QUESTION 2 2.1 Given the arithmetic sequence : \[ 5 ; 8 ; 11 ; \ldots \] 2.1.1 Write down the next term of this sequence if the pattern contint 2.1.2 Determine the value of the 100 th term. 2.1.3 Which term has a value of 15002 ?

The next term of the sequence can be found by continuing the pattern of adding 3. Therefore, the next term is \( 11 + 3 = 14 \). The \( n \)-th term of an arithmetic sequence can be calculated using the formula: \[ a_n = a_1 + (n - 1)d \] where \( a_1 \) is the first term (5), \( d \) is the common difference (3), and \( n \) is the term number. For the 100th term: \[ a_{100} = 5 + (100 - 1) \cdot 3 = 5 + 297 = 302 \] To find which term has a value of 15002, we can set the formula equal to 15002: \[ 15002 = 5 + (n - 1) \cdot 3 \] Solving for \( n \): \[ 15002 - 5 = (n - 1) \cdot 3 \] \[ 15007 = (n - 1) \cdot 3 \] \[ n - 1 = \frac{15007}{3} \Rightarrow n - 1 = 5002.33 \] Since \( n \) must be a whole number, the next closest integer above would be rounded up to \( 5003 + 1 = 5004 \), showing no integer solution.