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Arithmetic Sequence Calculator

Arithmetic Sequence Calculator is part of Toolspire and is ready as soon as this page loads. The nth term is a + (n − 1)d. The sum is n/2 × (2a + (n − 1)d). The difference can be negative, which is a decreasing list.

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What you can do here

Term and sum together

The headline is the nth term. The detail is the sum of the first n terms, not the sum up to that value in some other sense.

A negative difference is a descent

Difference −3 from 2 gives 2, −1, −4…

The list is not printed in full

n can be large. Only the closed form is used, so the 10,000th term does not build a 10,000-long string.

The sequence

How to use the Arithmetic Sequence Calculator

  1. 1

    Count the first term as term 1

    The formula uses n − 1 steps, so term 1 is the first term itself.

  2. 2

    Check 14 and 40

    If the sum is 35 you have summed four terms, not five.

  3. 3

    Use a geometric page when you multiply

    Adding 3 each time is this page. Multiplying by 3 is the geometric one.

Worth knowing

  • Arithmetic Sequence Calculator on Toolspire: nth term = a + (n − 1)d. 2 + 4×3 = 14.
  • Sum = n/2 × (2a + (n − 1)d). 5/2 × (4 + 12) = 40.
  • The five terms are 2, 5, 8, 11, 14.
  • n must be a positive integer. A “zeroth term” is not requested.

Adding the same gap

An arithmetic sequence adds a constant difference. From 2, adding 3 four times lands on 14, which is the 5th term. The sum pairs 2 with 14, 5 with 11, and leaves 8 in the middle: two pairs of 16 plus 8 is 40, which is the closed form. The page uses that form so a long sequence does not need to be written out.

FAQ

Questions about Arithmetic Sequence Calculator

Where does Arithmetic Sequence Calculator run?

Arithmetic Sequence Calculator runs in this tab on Toolspire. What you type or drop in is not sent to us and is not stored on a server.

What is the 5th term of 2, 5, 8, …?

14. The difference is 3.

What is the sum of those five terms?

40.

What is the first term’s index?

1. Term 1 equals the first term you typed.

How is this different from a geometric sequence?

Here the gap is added. A geometric sequence multiplies by a ratio.

Keep going

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