# Arithmetic sequences

An arithmetic sequence is a sequence in which the difference between two consecutive terms is constant

Simply put, the next term is obtained by adding a certain number to the previous one. This number is constant, that is, it stays the same all the time.

# 2,5,8,11,14,...

Above is an arithmetic sequence, since the difference between two consecutive terms is 3. This number is denoted by** ***d** *also known as the common difference. The sequence would continue 17,20,23,26, ...

**Example 1**

The first term of an arithmetic sequence is 2 and the second term is 6. Work out the next two terms of the sequence.

### General term

In an arithmetic sequence we have *d* which is added to a term to get the next term.

To get the second term, we add *d* to the first term. To get the third term we add *d* again, that is, to the first term we add *d** * twice to get the third term. The fourth term is obtained by adding

*d*three times to the first term. And so on.

Therefore, we can get any term by adding *d* to the first term one time less than the order number of that term we are seeking.

**Example 2**

The first term of an arithmetic sequence is 2 and the second term is 6. Work out the tenth term of the sequence.

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