QUESTION 7 Look at this sequence \( 3 ; 6 ; 11 ; 18 ; 27 ; \ldots ; \ldots ; \) 7.1. Write the next 2 terms 7.2. In the pattern \( 7 ; 11 ; 15 ; 19 ; \ldots ; \) 7.2.1. Find the constant difference 7.2.2. Describe the patterns in your own
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To find the next two terms in the sequence \( 3; 6; 11; 18; 27; \ldots \), we first identify the differences between consecutive terms: \( 3, 5, 7, 9 \). The differences are increasing by 2. Continuing this pattern, the next difference would be \( 11 \), leading to \( 27 + 11 = 38 \). The next difference after that would be \( 13 \), leading to \( 38 + 13 = 51 \). So, the next two terms are \( 38 \) and \( 51 \). For the sequence \( 7; 11; 15; 19; \ldots \), the constant difference is \( 4 \) (as each term increases by 4). In this linear sequence, each term is derived by adding consecutive increments of 4, showcasing a steady climb through each number. This is like a staircase where each step represents a consistent addition, leading to an easy prediction of future numbers!