We compare each term in the 4 times table to see what we need to adjust it by to make our sequence. Since the terms in this example increase by 4, we write a 4 in front of the n. The number in front of the n in the nth term formula tells us how much we are increasing or decreasing by. We can see that we subtract 1 from each term in the 4n sequence to make the original sequence and so, the nth term is 4n – 1. For example 3, 7, 11, 15, 19… increase by 4 each time so we start with the 4n sequence: 4, 8, 12, 16, 20. Then list multiples of the difference and see what needs to be added or subtracted to this to make the original sequence. Start by writing this difference multiplied by n. To find the nth term of an arithmetic sequence, find the common difference between each term. How to Find the Nth Term of an Arithmetic Sequence For example, with -2n + 10, the terms decrease by 2 each time. The number in front of the n in the nth term for a decreasing arithmetic sequence tells us how much the terms decrease by each time. This is because the number in front of the n is -2.ĭecreasing arithmetic sequences always decrease by the same amount from one term to the next. For example, the arithmetic sequence formed by -2n + 10 starts at 8 and goes down by 2 each time. The same can be seen in the 3 times table with the 3n sequence.Īgain, the 3 times table goes up in threes and is formed by writing a 3 in front of the n.Īrithmetic sequences can also decrease from one term to the next. We add 5 to get from one number to the next. We can see that the common difference between the terms in the 5 times table is 5. Substituting n = 1, n =2 etc into the 5n sequence we get 5, 10, 15, 20 and so on. We can form sequences for the times tables by writing the appropriate number in front of n.įor example, the nth term for the 5 times table is just 5n. The most basic arithmetic sequences are the times tables. The terms increase by 2 each time because there is a 2 in front of the n in the formula. The number in front of the n in the arithmetic sequence formula tells us what the difference is between each term in the sequence.įor example in the sequence above, the nth term is 2n + 1. We add 2 from one term to the next and so, the common difference is 2. For example, the sequence of 3, 5, 7, 9, 11… is arithmetic because the difference between each term is 2. We say that in an arithmetic sequence, there is a common difference between the terms. Here is a table showing the first ten terms of the sequence 3n + 2 using the nth term formula.Īn arithmetic sequence is a list of numbers that always increase or decrease by the same amount from one number to the next. Here is a list of calculations for generating the first 5 terms of the sequence 3n + 2. To generate a sequence using the nth term, substitute consecutive values of n into the sequence starting from n = 1. The nth term can be used to generate a sequence. 3 × 10 + 2 = 32 and so, the tenth term of the sequence is 32. For example, if the nth term is 3n + 2, the 10th term of the sequence can be found by substituting n = 10 into the nth term. To find a given term, substitute the corresponding value of n into the nth term formula. The nth term is a formula used to generate any term of a sequence.
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