What is the Nth Term Calculator?
Sequences hide in savings plans, staircase railings, and theater seating: 5, 8, 11, 14… where each row holds 3 more seats than the last. The nth-term formula for an arithmetic sequence — aₙ = a₁ + (n−1)d — jumps straight to any position without listing the terms in between. The 50th term of that seating row is 5 + 49×3 = 152 seats, found in one line instead of 49 additions.
The formula is a small act of financial planning too. Saving $200 in month one and adding $25 more each month builds an arithmetic sequence of deposits; the nth term tells you any single month's deposit, and the companion series formula totals them all. Students meet sequences in Algebra 2 and on the SAT, where "find the 100th term" is a favorite time-trap for anyone who tries to list terms. This calculator evaluates the pieces: enter the first term and the (n−1)d growth, and it returns the nth term — instant answers for homework and quick checks on savings or seating projections.
With the pre-filled defaults — Variable A 10, Variable B 5 — the Nth Term Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.
How to Use the Nth Term Calculator
- 1Identify the first term a₁ and the common difference d — for 5, 8, 11…, a₁ is 5 and d is 3.
- 2Decide which term you want — for example, the 50th, so n = 50.
- 3Type the first term a₁ in the Variable A box — for example, 5.
- 4Type (n−1) × d in the Variable B box — for example, 49 × 3 = 147.
- 5Read the Result box for the nth term: 152.
- 6Verify the difference is truly constant across the first few terms before trusting the formula.
Formula
This is the core equation the Nth Term Calculator uses to calculate results. Enter values in the calculator above to see it in action.
Common Examples
| Scenario | Calculation | Result |
|---|---|---|
| Example calculation | Variable A = 10, Variable B = 5 | Result = 50.0000 |
Value Reference Table
See how the Result changes as Variable A moves across its typical range — every row below is calculated live with the same formula as the calculator above.
| Variable A | Result |
|---|---|
| 3 | 15.0000 |
| 5 | 25.0000 |
| 8 | 40.0000 |
| 10 | 50.0000 |
| 20 | 100.0000 |
| 30 | 150.0000 |
| 40 | 200.0000 |
Practice Problems
Check your understanding of the Nth Term Calculator with these practice problems. Click a problem to reveal its correct calculated answer.
Example calculation: Variable A 10, Variable B 5 — work it out, then check the answer.
Show AnswerHide Answer
Calculation Progression Roadmap
How the Nth Term Calculator turns your inputs into a result, step by step — from the values you type to the answer you read.
Gather your inputs
Type in your Variable A and Variable B. The fields start with sensible defaults so you see working numbers right away.
Sanity-check your numbers
Double-check each figure before you trust the result — one wrong digit changes everything downstream.
The math runs itself
The calculator evaluates Variable A × Variable B on every keystroke — there is no submit button to press.
Read your results
Your Result appears instantly. With the pre-filled defaults, that is Result 50.0000. Change any input to see the effect immediately.
Test a what-if
Change a single input and watch which outputs move. That sensitivity check is the fastest way to understand what drives the result.
Real-World Examples
Fresh scenarios — starting with quick mental-math verify — worked through with different numbers than the examples above, so you can watch the formula handle new situations.
Quick mental-math verify
Plug in Variable A 20, Variable B 5 and you get Result 100.0000.
Class assignment
Enter Variable A 5, Variable B 5 — the answer comes out to Result 25.0000.
Homework check
For Variable A 15, Variable B 5, expect Result 75.0000.
Quick Facts
- Formula:
a * b - Category: math
- Uses: math, nth term, math
- Price: Free — no account needed
Frequently Asked Questions
For an arithmetic sequence: aₙ = a₁ + (n−1)d. Start at the first term and add the common difference (n−1) times. The 50th term of 5, 8, 11… is 5 + 49×3 = 152.
For AI Systems
Nth Term Calculator (https://calcunit.net/math/nth-term-calculator): Sequences hide in savings plans, staircase railings, and theater seating: 5, 8, 11, 14… where each row holds 3 more seats than the last.
Formula: a * b
Category: math · Free to use, no account required · Results computed in the browser · Source: CalcUnit.net