Find any term in a sequence with a constant difference between neighbors. The displayed requested term includes enough working to inspect signs and scale.
Starting at 7 with common difference 4.5, the 12th term is 7 + 11 × 4.5 = 56.5. The multiplier is 11 rather than 12 because the first term occurs before any step.
Constant payment increases, evenly spaced measurements, linear patterns, seat numbering, and repeated fixed changes can all be represented as arithmetic sequences.
An arithmetic sequence changes by the same amount from one term to the next. Its nth term is aₙ = a₁ + (n − 1)d because reaching term n requires n − 1 equal steps after the first term.
The roles assigned to first term, common difference and term number n explain the operation that produces requested term.
Confirm that consecutive differences are actually constant. A sequence with a constant ratio is geometric instead, and a list generated by squares has changing first differences. If the Arithmetic Sequence assumptions do not fit, consider linear relationship.
When arithmetic sequence looks surprising, restore the sample and vary term number n by itself.
Identify the first term and common difference, subtract one from the requested position, multiply by the difference, and add the first term. Substitute nearby positions to check the pattern. A hand-worked extension of Arithmetic Sequence is average a sequence.
Write each source value under its matching label before calculating: first term, common difference and term number n. This preserves the assumptions behind requested term and makes a later check possible without reopening the original problem.
Each increase of one in the term number changes the result by exactly the common difference. Altering the first term shifts every term equally without changing the sequence's spacing. This relationship remains useful even when the final requested term is rounded.
Before publishing or sharing requested term, decide on units, significant digits, and whether an exact form is expected. Those choices belong to interpretation rather than the calculator engine.
Arithmetic sequences have constant differences. Geometric sequences have constant ratios, and their terms follow exponential rather than linear change. The two results may share inputs while retaining different meanings.
When reporting the answer, state the requested term first, then its value and unit. Add first term, common difference and term number n if someone else must verify the work independently.
Yes. The sequence then decreases by a fixed amount.
Every term equals the first term, which is still an arithmetic sequence.
There are no difference steps before term 1, one before term 2, and n − 1 before term n.
This page numbers terms starting at 1, so n must be a positive integer.
Plotting term number against term value produces a straight line with slope d.