sequences: (a) a1 12 and a n an 1 2 for n 2 (b) a1 5 and an 2an. The terms of the sequence will alternate between positive and negative. quadratic recurrence relation an (an 1) 2 2 for n 2. (c) Identify the formula for the nth term of a simple geometric sequence (e.g nth term of 2, 4, 8, 16. Some of the terms of this sequence are surds, so leave your answer in surds as this is more accurate than writing them in decimal form as they would have to be rounded. (b) Find/use nth term of a quadratic sequence. I have always taight zero term method for linear and incorporated that into quadratic but having read your notes, I am going to teach them your way today. (-1) in your explanation of the quadratic sequence (bottom line). Continuing, the third term is: a3 r ( ar) ar2. Since we get the next term by multiplying by the common ratio, the value of a2 is just: a2 ar. Show that the sequence 3, 6, 12, 24, … is a geometric sequence, and find the next three terms.ĭividing each term by the previous term gives the same value: \(\frac\). GCSE Term-to-term sequences & Arithmetic vs Geometric Progressions. For geometric sequences, the common ratio is r, and the first term a1 is often referred to simply as 'a'. In a \(geometric\) sequence, the term to term rule is to multiply or divide by the same value.
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