An arithmetic sequence is one in which a term is obtained by adding a constant to a previous term of a sequence. So the n th term can be described by the formula an=an−1+d a n = a n − 1 + d . A geometric sequence is one in which a term of a sequence is obtained by multiplying the previous term by a constant.
What are the terms of a sequence?
A sequence is a list of numbers in a certain order. Each number in a sequence is called a term . Each term in a sequence has a position (first, second, third and so on). For example, consider the sequence {5,15,25,35,…} In the sequence, each number is called a term.
How to find the next term in a sequence?
Firstly, work out the difference in the terms. This sequence is going up by four each time, so add 4 on to the last term to find the next term in the sequence. 3, 7, 11, 15, 19, 23,
Which is the first number in the sequence?
The first number is 3. The term to term rule is ‘add 4’. Once the first term and term to term rule are known, all the terms in the sequence can be found.
What’s the difference between the first and second terms in an arithmetic sequence?
The difference between the first and second terms is 1, and the difference between the second and third terms is also 1. However, the difference between the third and fourth terms is 3. Because the difference is not common for the entire list, then this is not an arithmetic sequence. Add the common difference to the last given term.
When is a sequence called a geometric sequence?
If the rule is to multiply or divide by a number each time, it is called a geometric sequence. Each number in a sequence is called a term. A sequence which increases or decreases by the same amount each time is called a linear sequence. The term to term rule of a sequence describes how to get from one term to the next.
