![]() ![]() The terms of the sequence will alternate between positive and negative. 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. An arithmetic sequence is a sequence of numbers where each new term after the first is formed by adding a fixed amount called the common difference to the. The sequence 1, 4, 7, 10, 13, 16 is an arithmetic sequence with a difference of 3 in its successive terms. Example 2 Identifying aand din an arithmetic sequence For the. Rule for nding the nth term in an arithmetic sequence The nth term of an arithmetic sequence is given by t n a +(n 1)d where a ( t 1)isthe value of the rst term andd is the common difference. ![]() ![]() 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: \(\frac\). Arithmetic vs Geometric Sequence Examples Examples of Arithmetic. This gives us the following rule for the nth term of an arithmetic sequence. A geometric sequence goes from one term to the next by always multiplying (or dividing) by the same value. xn a + d (n-1) (We use 'n-1' because d is not used in the 1st term). In a \(geometric\) sequence, the term to term rule is to multiply or divide by the same value. Example Show that the sequence 3, 6, 12, 24, is a geometric sequence, and find the next three terms. ![]()
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