2.1 Given the combined arithmetic and constant sequences: \( 3 ; 2 ; 6 ; 2 ; 9 ; 2 ; \ldots, 2 \) 2.1.1 Write down the next two terms in the sequence. 2.1.2 Calculate the sum of the first 100 terms of the sequence.

The next two terms in the sequence are \( 12 \) and \( 2 \). The pattern follows the structure where every third term increases by \( 3 \) while the other terms remain constant at \( 2 \). To calculate the sum of the first 100 terms, we note there are 33 complete cycles of the pattern \( 3, 2, 6, 2, 9, 2 \) with the first term repeating once more, plus one additional \( 2 \) to make it a total of \( 100 \). The sum of one cycle is \( 3 + 2 + 6 + 2 + 9 + 2 = 24 \). Hence, the sum for 33 cycles is \( 33 \times 24 = 792 \), and adding the \( 2 \) from the last incomplete cycle gives \( 794 \). Thus, the sum of the first 100 terms is \( 794 \).