Exercise Question 2 (Page 188)

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Exercise Question 2 (Page 188) Can you find a recursive rule for the formula 𝑡_𝑛=3 × 10^(𝑛−1) that generates the geometric progression 3, 30, 300, 3000,… ? A recursive formula tells you how to find the next term in a sequence by doing something to the previous term. It always requires two pieces of information The starting point (usually the first term, a) The rule to get from one term (an–1) to the next term (an) For any GP, our recursive rule is an = an–1 × r, a1 = a Given our nth term 𝒕_𝒏=𝟑 × 〖𝟏𝟎〗^(𝒏−𝟏) And, GP 3, 30, 300, 3000, … Thus, First term = a = 3 Common ratio = r = 30/3 = 10 Thus, our recursive rule is 𝒕_𝟏=𝟑,𝒕_𝒏=𝟏𝟎 × 𝒕_(𝒏−𝟏) ( for 𝒏≥𝟐). 3, 30, 300, 3000, … Thus, First term = a = 3 Common ratio = r = 30/3 = 10 Thus, our recursive rule is 𝒕_𝟏=𝟑,𝒕_𝒏=𝟏𝟎 × 𝒕_(𝒏−𝟏) ( for 𝒏≥𝟐)