Common difference is the constant number you add or subtract to move from one term to the next in an arithmetic sequence. In Intermediate Algebra, it is written as d and helps you find missing terms or write formulas.
Common difference is the fixed amount between consecutive terms in an arithmetic sequence in Intermediate Algebra. If the sequence goes 4, 7, 10, 13, the common difference is 3 because each term is 3 more than the one before it.
You find it by subtracting one term from the next term. That means 7 minus 4 equals 3, 10 minus 7 equals 3, and 13 minus 10 equals 3. If the same difference keeps showing up, the pattern is arithmetic. If the differences change, then it is not an arithmetic sequence.
The common difference is usually written as d. A positive d makes the sequence increase, while a negative d makes it decrease. For example, 20, 15, 10, 5 has a common difference of -5 because you subtract 5 each time.
This term matters because arithmetic sequences are all about constant change. In Intermediate Algebra, that idea connects sequence tables, recursive rules, and explicit formulas. If you know the first term and the common difference, you can keep extending the pattern or jump straight to any term.
A common mistake is mixing up the order when you subtract. For the sequence 12, 9, 6, 3, the common difference is 9 - 12 = -3, not 12 - 9. The sign matters because it tells you whether the pattern is going up or down.
You can also think of common difference as the sequence version of slope. The terms change by the same amount each time, just like a linear pattern changes by the same amount across equal steps. That is why arithmetic sequences often show up right next to linear patterns in class.
Common difference is the piece that lets you turn a number pattern into a rule. Once you know d, you can find the next term, check whether a sequence is arithmetic, and write formulas instead of listing every number by hand.
That matters a lot in Intermediate Algebra because sequences are one of the first places where you see repeated change in a formal way. If a teacher gives you a table or a list of terms, you use the common difference to test the pattern and decide whether the sequence follows an arithmetic rule.
It also connects to formulas. The explicit formula for an arithmetic sequence depends on the first term and d, so without the common difference you cannot build the rule correctly. Recursive formulas also use it directly, since each term is defined by adding the same value to the previous term.
Common difference shows up any time you need to extend a pattern, describe a linear pattern in words, or solve for a missing term in a sequence problem. It is one of the quickest ways to spot whether the sequence is steady and predictable or changing in some other way.
Keep studying Intermediate Algebra Unit 12
Visual cheatsheet
view galleryArithmetic Sequence
An arithmetic sequence is the setting where common difference lives. If the gap between every pair of consecutive terms stays the same, the sequence is arithmetic and that gap is the common difference. When the gap changes, you are looking at a different kind of sequence, not an arithmetic one.
Recursive Formula
A recursive formula tells you how to get each term from the one before it, and for arithmetic sequences that rule uses the common difference. For example, you might say each term equals the previous term plus d. That makes the common difference the engine behind the step-by-step pattern.
Explicit Formula
An explicit formula lets you find any term without listing the ones before it. In arithmetic sequences, the formula depends on the first term and the common difference. If you know d, you can jump to term number 20 or term number 100 without writing every earlier term.
Constant Rate of Change
Common difference is the sequence version of constant rate of change. Both mean the amount of change stays the same from step to step. In algebra, that idea helps connect sequences to linear patterns and makes it easier to compare tables, graphs, and formulas.
A quiz or problem set might give you a sequence and ask you to identify the common difference, complete missing terms, or decide whether the sequence is arithmetic. You may need to subtract consecutive terms carefully and show that the difference stays the same across the whole list. If the sequence is written in a table or word pattern, the job is still the same, find the repeated change. A frequent trap is using the wrong subtraction order and getting the sign wrong, which changes the answer from increasing to decreasing. If you know d, you can also use it to write the next few terms or set up an explicit or recursive formula.
Common difference is for arithmetic sequences, where you add or subtract the same amount each time. Common ratio is for geometric sequences, where you multiply by the same number each time. If the pattern uses repeated addition, think difference. If it uses repeated multiplication, think ratio.
Common difference is the constant amount added or subtracted between consecutive terms in an arithmetic sequence.
You find it by subtracting one term from the next, and the sign tells you whether the sequence increases or decreases.
If the common difference stays the same, the sequence is arithmetic.
The value of d is what lets you extend the sequence, write formulas, and fill in missing terms.
A wrong subtraction order can flip the sign, so always check your consecutive terms carefully.
Common difference is the fixed number that separates each term in an arithmetic sequence from the next one. In Intermediate Algebra, you usually write it as d. If the sequence is 2, 5, 8, 11, the common difference is 3 because each term goes up by 3.
Subtract one term from the next term in the sequence. For 18, 14, 10, 6, you get 14 - 18 = -4, so the common difference is -4. Check more than one pair if you want to make sure the sequence really is arithmetic.
No. Common difference means you add or subtract the same amount each time, which is arithmetic. Common ratio means you multiply by the same amount each time, which is geometric. That difference changes how you find future terms and which formula you use.
Take the last term and add the common difference. If the sequence is 9, 12, 15, and d = 3, the next term is 18. If d is negative, you subtract instead, like 20, 16, 12, next term 8.