Arithmetic Sequence Calculator
Solve any arithmetic sequence. Find the nth term, common difference, term count, or sum from any three known values. Shows the first 10 terms.
Arithmetic Sequence
Given first term, common difference, and number of terms.
Nth term (a_n)
29
Sum (S_n)
155
First term (a_1)
2
Common difference (d)
3
Term count (n)
10
First 10 terms
2, 5, 8, 11, 14, 17, 20, 23, 26, 29
Frequently Asked Questions about the Arithmetic Sequence Calculator
What is the formula for an arithmetic sequence?
The nth term is a_n = a_1 + (n - 1) x d, where a_1 is the first term, d is the common difference, and n is the position. Each term is the previous term plus d.
How is an arithmetic sequence different from a geometric one?
An arithmetic sequence adds a fixed amount (d) between terms. A geometric sequence multiplies by a fixed ratio (r). 2, 5, 8, 11 is arithmetic with d = 3. 2, 6, 18, 54 is geometric with r = 3.
Where do arithmetic sequences show up in real life?
Anywhere a quantity grows by a fixed step: simple interest payments, stadium seating rows, monthly savings deposits of the same amount, depreciation in equal increments, and the floor numbers in a building.
How is the sum formula derived?
Write the sum forward and backward, then add the two rows term by term. Every column sums to (a_1 + a_n), and there are n columns, so 2 x S_n = n x (a_1 + a_n). Divide by 2 to get S_n = n/2 x (a_1 + a_n).
Can an arithmetic sequence have an infinite sum?
No finite sum, unless d = 0 and a_1 = 0. For any non-zero d, the terms grow without bound (positively or negatively), so the partial sums diverge. Use this calculator for finite n only.