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Given the first term and the common difference of an arithmetic sequence, find the first several terms.
Write the first five terms of the arithmetic sequence with and .
Adding is the same as subtracting 3. Beginning with the first term, subtract 3 from each term to find the next term.
The first five terms are
List the first five terms of the arithmetic sequence with and .
Given any the first term and any other term in an arithmetic sequence, find a given term.
Given and , find .
The sequence can be written in terms of the initial term 8 and the common difference .
We know the fourth term equals 14; we know the fourth term has the form .
We can find the common difference .
Find the fifth term by adding the common difference to the fourth term.
Some arithmetic sequences are defined in terms of the previous term using a recursive formula . The formula provides an algebraic rule for determining the terms of the sequence. A recursive formula allows us to find any term of an arithmetic sequence using a function of the preceding term. Each term is the sum of the previous term and the common difference. For example, if the common difference is 5, then each term is the previous term plus 5. As with any recursive formula, the first term must be given.
The recursive formula for an arithmetic sequence with common difference is:
Given an arithmetic sequence, write its recursive formula.
Write a recursive formula for the arithmetic sequence .
The first term is given as . The common difference can be found by subtracting the first term from the second term.
Substitute the initial term and the common difference into the recursive formula for arithmetic sequences.
Do we have to subtract the first term from the second term to find the common difference?
No. We can subtract any term in the sequence from the subsequent term. It is, however, most common to subtract the first term from the second term because it is often the easiest method of finding the common difference.
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