Work out the nth term of the following sequence: 3, 5, 7, 9, Firstly, write out the sequence and the positions of the terms. As there isn't a clear way of going from the position to the term, look for a common difference between the terms. In this case, there is a difference of 2 each time. This common difference describes the times tables that the sequence is working in. In this sequence it's the 2 times tables.
Write out the 2 times tables and compare each term in the sequence to the 2 times tables. To get from the position to the term, first multiply the position by 2 then add 1. Position to term rules or nth term Each term in a sequence has a position.
We can make a sequence using the nth term by substituting different values for the term number n. In this lesson, we will look specifically at finding the n th term for an arithmetic or linear sequence.
Includes reasoning and applied questions. To find out more about the different types of sequences, and how to answer sequence related questions you may find it helpful to look at the introduction to sequences lesson or one of the others in this section. To find the nth term, first calculate the common difference , d.
Then add or subtract a number from the new sequence to achieve a copy of the sequence given in the question. Find the common difference for the sequence. Add or subtract a number to obtain the sequence given in the question. Here, we generate the sequence 0. The n th term of this sequence is 0.
Find the n th term for the sequence For example, taking the decreasing sequence -2, -4, -6, -8, , … which has the n th term of -2n but is incorrectly stated as 2n which would be an increasing sequence. This is also true with the constant. Write down the first three terms in the sequence 4n Below is a table describing the position of each term in an arithmetic sequence and the value of these terms.
The common difference here is 5 so it is 5n. The common difference is so it is n. We do not need to add or subtract anything here so the nth term is just n. The number of petals on a sunflower can be represented as a linear sequence. Write an expression for the number of petals on sunflower n. The number of petals on the first three flowers are 5, 7 and 9. The common difference is 2 so it is 2n.
The number of square tiles around a pool generates an arithmetic sequence. How many tiles would there be around a pool of width 30? Around the first three pools, the number of tiles are 8, 12 and Sequence 1, 3, 5, 7 — common difference is 2. Show how you decide. Common difference is 3. Yes it is the 36th term. There are two numbers under 30 that appear in both sequences.
What are the two numbers? Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors. Find out more about our GCSE maths revision programme. N th term examples. Common misconceptions. Learning checklist. Next lessons. Still stuck? In order to access this I need to be confident with: Addition and subtraction Multiplication and division Substitution Arithmetic sequences.
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