![]() ![]() Students will be given the first 5 terms in the sequence and have to determine whether it is arithmetic or geometric and then write the explicit equation. The terms of the sequence will alternate between positive and negative. This 20-question puzzle provides students with practice writing explicit formulas for arithmetic and geometric sequences. They even have a nifty bit of notation - the exclamation mark. As you have noticed, it has a recursive definition: a 1, and a na Factorials crop up quite a lot in mathematics. An arithmetic-geometric progression (AGP) is a progression in which each term can be represented as the product of the terms of an arithmetic progressions. That sequence is the 'factorial' numbers. 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. You're right, that sequence is neither arithmetic nor geometric. The sequence is indeed a geometric progression where a1 3 and r 2. 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: \(\frac\). In a \(geometric\) sequence, the term to term rule is to multiply or divide by the same value.
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