Any term in the sequence can then be found by substituting its position number into the formula for un. The 1st term is then called u1, the 2nd term u2, the 3rd term u3, the 4th term u4, the 5th term u5 and so on. Writing sequences from position-to-term rules The nth term, or the general term, of a sequence is often called un. What is the 20th term in this sequence? 202 = 400 1 4 9 16 25 Each term can be found by squaring its position in the sequence. For example, The nth term in a sequence is n2, where n is the term’s position in the sequence. Sequences from position-to-term rules Position 1st 2nd 3rd 4th 5th … nth Term … n2 When a sequence is defined by a position-to-term rule it can sometimes help to put the terms in a table. Sequences from term-to-term rules Write the first five terms of each sequence given the first term and the term-to-term rule. ![]() Position-to-term rules are harder to find for a given sequence but are more useful for finding any term in a sequence. Term-to-term rules are usually easier to find for a given sequence. To define a sequence using a position-to-term rule we use a formula for the nth term of the sequence. To define a sequence using a term-to-term rule we need to know the first term in the sequence and what must be done to each term to give the value of the next term. The second is to use a position-to-term rule. How could this sequence continue? 14 22 32 44 16 32 64 128ĭefining sequences The first is to use a term-to-term rule. For example, a sequence starts with the numbers 2, 4, 8. Predicting terms in a sequence +2 +4 +6 +8 +10 +12 2 4 8 ×2 ×2 ×2 ×2 ×2 ×2 2 4 8 If we are not given the rule for a sequence, or if it is not generated from a practical context, we cannot be certain how it will continue. We can use this to find the next two terms. 67 60 We can predict that this sequence continues by subtracting 7 each time. Look at the difference between each consecutive term. ? –7 –7 –7 –7 –7 –7 102 95 88 81 74 Sometimes, we can predict how a sequence will continue by looking for patterns. Predicting terms in a sequence For example, What are the next two terms in the following sequence, 102, 95, 88, 81, 74. For example, If terms are next to each other they are referred to as consecutive terms. Each number in a sequence is called a term. ![]() In mathematics, a sequence is a succession of numbers that follow a given rule.
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