Pay attention to whether the 1 is being added or subtracted to decide which term the notation is referring to. If a_1 is the first term, the successive terms of the geometric sequence follow this same pattern. The first term of the sequence should always be defined, and is often a_1. Since sequence notation looks similar to other types of mathematical notation, such as exponential notation, it can be easy to confuse them. This means that even though the sequence is showing negative integers rather than positive integers, it is still increasing. Practice with our Extend arithmetic sequences exercise. For example, if we start with 5 and have a common difference of 3, our sequence will be 5, 8, 11, 14, 17, 20. This is the number we will add to each term in order to get the next term. This sequence has a constant difference of +8. Start with the first term of the sequence, which can be any number. But not necessarily if the terms are negative. If the common difference is negative, this is true.
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