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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