The next three terms of the sequence are \(–16 \times –2 = 32\), \(32 \times –2 = −64\), and \(–64 \times –2 = 128\). There are 4n+1 terms in a sequence of which first 2n+1 are in Arithmetic Progression and last 2n+1 are in Geometric Progression in which the common difference. 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.
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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