The following sequence is a combination of arithmetic and geometric sequence: \( \begin{array}{llll}3 ; 3 ; 9 ; 6 ; 15 ; 12 ; \ldots \\ \text { 4.1.1 Write down the next TWO } & \text { (2) L1 } & \text { 4.1.2 Determine } T_{20}-T_{21}\end{array} \)

To determine the next two terms in the sequence, let’s break it down. The alternating pattern suggests that every other term forms an arithmetic sequence, while the others form a geometric one. The arithmetic sequence can be observed as: 3, 6, 9, 12 (which increases by 3). So the next term is 15. The geometric sequence is: 3, 9, 15 (which appears to multiply by 3, and then increases by 6). Continuing this pattern, the next term becomes \( 15 \times (3/2) = 22.5 \). Thus, we predict the next two terms are 15 and 18 for the arithmetic and 22.5 and 27 for the geometric. Now, moving on to \( T_{20} - T_{21} \): To find these terms, we note the pattern continues: The 20th arithmetic term is 3 + (19 × 3) = 60, and the 21st term follows the sequence down to 18 and assumed terminal growth, leading to \( 60 - 18 = 42 \). Thus, \( T_{20} - T_{21} = 42 \).