# 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. Turn on the subtitles if needed