# NTH Term of a Sequence?

A formula can be used when it is required to determine the exact number of a sequence without having to go from one number to the next. The formula is dn + (a - d) where d is the difference between two consecutive terms, a is the first term and n is the term number.
The 'nth' term is a method with 'n' in it which facilitates you to find any term of a series without having to go up from one term to another. 'n' stands for the term digit so to find the 10th term we would just replace 10 in the formula in place of 'n'.
The nth term in a sequence is found by using a formula that will depend on whether the sequence is a constant distance sequence or a changing difference sequence. For a changing difference sequence the formula for getting the nth term is a + (n - 1)d + ½(n - 1)(n - 2)c where c is the second difference while a is the first term and d is the first difference. For a common difference sequence, the nth term is found by using the formula dn + (a - d) where d is the common difference.
You will find the nth term for a constant difference sequence by getting the difference for the first term and the difference and then adding the answer to the multiple of the difference and the number of terms. You calculate the nth term for a changing difference sequence using the formula nth term = a + (n - 1) d + ½ (n - 1) (n - 2)c, where a is the first term, n is the number of terms in the series, d is the first difference of the first two terms and c is the second difference.
In a sequence, there is a noticeable pattern, therefore the first step is to discover the pattern then find the nth term by applying the pattern. For example; What is the nth term of the sequence 2, 5, 10, 17, 26... ? you will notice that the pattern involves adding odd numbers to the previous number.
Q&A Related to "NTH Term of a Sequence?"
 1. Check that the sequence you have is a cubic sequence by taking the difference between each consecutive pair of numbers (called the "method of common differences" Continue http://www.ehow.com/how_8545572_nth-term-cubic-seq...
 Finding the nth term is much simpler than it seems. For example, say you had the sequence: 1,4,7,10,13,16 Sequence 1. First we find the difference between the numbers. 1 (3) 4 (3) http://wiki.answers.com/Q/How_do_you_find_the_nth_...
 the general form of an arithmetic sequence with common difference d: a(n) = a(1) + d(n - 1) we have: a(n) = 3 + 6(n - 1) a(n) = 6n - 3. furthermore: S(n) = 6∑k - 3∑1. (summation http://answers.yahoo.com/question/index?qid=201310...
 There really is no general way. It's a case of trying different possibilities. First, take a general look at the sequence. Is there a constant difference? e.g. 3,7,11,15 ... then http://uk.answers.yahoo.com/question/index?qid=201...
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To get the nth term of a sequence of numbers you will have to use the formula f(n) = f(1) + (n-1)d, where f(1) is the first term, d is the common difference, and ...
1. Check that the sequence you have is a cubic sequence by taking the difference between each consecutive pair of numbers (called the "method of common differences ...
1. Check that the sequence you have is a cubic sequence by taking the difference between each consecutive pair of numbers (called the "method of common differences ...