The value of a given term of a linear sequence can be worked out using the general term of the sequence. The general term is also known as the nth term, because, for any term n in the sequence, the value of the term can be worked out.
To work out what the nth term of a sequence is, work out the common difference. Given the sequence 4, 7, 10, 13, ..., work out the difference between each value:
Next, find out the value of the zeroth term, by subtracting the difference from the value of the first term:
Any term can now be worked out:
difference x term + zeroth term value.
The nth term is 3n + 1 (3 is the difference, and 1 is the value of the zeroth term).
For any term, its value can be worked out by substituting the n with the term number.
For the value of the 30th term in the sequence 3n + 1: replace n with 30 and calculate 3 x 30 + 1 = 91.
1. What is the general term (nth term) for the sequence 2, 0, -2, -4?
Answer: -2n + 4
Set out a table:
The difference is -2, and the value of the nterm is 4. The nth term is -2n + 4
2. Is 32 a number in the sequence given by 3n - 5?
Set the question as an equation: 32 = 3n - 5.
37 = 3n (added 5 to both sides)
12.33 = n (divided both sides by 3)
Because 12.33 is not a whole number it cannot be a term; therefore 32 is not in the sequence.