Mathematica Grade 12 Capricorn South / Investigation Term / 2024 INVESTIGATTON \#I A sequence is defined by \( T_{1}=3 \) and \( T_{k+1}=T_{k}+3 \) for \( k \geq 1 \) a) Determine the first five terms of the sequence b) Show that the difference between any two successive terms is a constant. c) Prove that \( T_{k+1}-T_{k} \) is the common difference if \( k \in N \) d) What can you conclude?
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\( T_1 = 3 \) \( T_2 = T_1 + 3 = 3 + 3 = 6 \) \( T_3 = T_2 + 3 = 6 + 3 = 9 \) \( T_4 = T_3 + 3 = 9 + 3 = 12 \) \( T_5 = T_4 + 3 = 12 + 3 = 15 \) So, the first five terms of the sequence are 3, 6, 9, 12, and 15. Show more…
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