Sequence Calculator
What the Sequence Calculator Does
An arithmetic sequence grows or shrinks by the same fixed step at every position, and this calculator generates the whole run for you. Algebra students, teachers building examples, and savers modeling deposits that rise by equal amounts rely on it.
The Arithmetic Formula and a Worked Example
Every term obeys the n-th term rule a + (n – 1)d, where a is the Starting number and d is the common difference. Take 2, 5, 8, 11 with d = 3: the fifth term equals 2 + 4 x 3, which is 14.
Totals follow the sum rule n/2 x (first + last). For five terms running 2 through 14, that is 5/2 x (2 + 14) = 40.
A savings plan puts the formula to work. Suppose a deposit starts at 100 and rises by 50 every month, giving 100, 150, 200 and onward; enter a Starting number of 100 and a Common difference of 50. The 12th deposit obeys a + (n – 1)d as 100 + 11 x 50 = 650, and the year’s total follows n/2 x (first + last): 12/2 x (100 + 650) = 4,500. Ask for the 12th term and the calculator lays out all twelve deposits in order.
How to Build Your Own Sequence
Choose Arithmetic under Sequence type, set Sequence direction to Increasing or Decreasing, and enter a Starting number plus the Common difference. Put your target in n-th term to obtain and press Calculate. Each term up to that point displays at once.
Tips: a negative difference shrinks the list. Starting at 20 with -4 gives 20, 16, 12, 8 and onward.
Frequently Asked Questions
What makes a sequence arithmetic?
The gap between neighboring terms never changes. In 2, 5, 8, 11 every step adds 3, so the pattern is arithmetic with common difference 3.
How do I reach the 10th term?
Multiply the difference by one less than the position and add the start. For 2, 5, 8, 11 the 10th term is 2 + 9 x 3 = 29.
How do I total all terms?
Average the first and last terms, then multiply by the count. For 2 through 14, the average is 8 and 8 x 5 gives 40.
Can the common difference be negative?
Yes, and the list then falls. Starting at 20 with a difference of -4 produces 20, 16, 12, 8, each term four smaller than the last.
Does the tool support Fibonacci?
It does, though a Fibonacci term equals the sum of the two before it rather than a fixed step, so choose that option and enter a starting number to begin.