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.
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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 \( 794 \).
