Find The Missing Term of The Following Arithmetic Sequence Calculator

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This constant difference is called the common difference. If you have an arithmetic sequence with one missing term, you can find it using the formula for the nth term of an arithmetic sequence.

What is an Arithmetic Sequence?

An arithmetic sequence is a sequence of numbers where the difference between each consecutive term is constant. This difference is known as the common difference, usually denoted by the letter 'd'.

Examples of arithmetic sequences include:

2, 5, 8, 11, 14 (common difference of 3)
10, 7, 4, 1, -2 (common difference of -3)
3, 3, 3, 3, 3 (common difference of 0)

In each of these examples, the difference between consecutive terms remains the same, which is the defining characteristic of an arithmetic sequence.

How to Find the Missing Term

To find the missing term in an arithmetic sequence, you need to know at least two other terms in the sequence. The most common scenario is when you know the first term and the common difference, and you need to find a term later in the sequence.

The general approach is:

Identify the position of the missing term in the sequence (its term number)
Use the formula for the nth term of an arithmetic sequence
Plug in the known values to solve for the missing term

This calculator automates this process for you, but understanding the underlying formula is important for verifying results and solving similar problems manually.

The Formula

Formula for the nth Term

The nth term of an arithmetic sequence can be found using the formula:

aₙ = a₁ + (n - 1) × d

Where:

aₙ = nth term
a₁ = first term
d = common difference
n = term number

This formula allows you to find any term in the sequence if you know the first term, common difference, and the position of the term you want to find.

For example, if you know the first term is 5, the common difference is 3, and you want to find the 4th term, you would calculate:

a₄ = 5 + (4 - 1) × 3 = 5 + 9 = 14

Worked Example

Let's find the missing term in the following arithmetic sequence: 7, 11, _, 17, 21

Step 1: Identify the known values

First term (a₁) = 7
Second term = 11
Fourth term = 17
Fifth term = 21

Step 2: Find the common difference (d)

The common difference is the difference between consecutive terms. Let's calculate it using the first two terms:

d = 11 - 7 = 4

Step 3: Find the missing term (third term)

We know the third term is the second term plus the common difference:

a₃ = a₂ + d = 11 + 4 = 15

So the complete sequence is: 7, 11, 15, 17, 21

Verification

To ensure our answer is correct, let's verify using the nth term formula:

a₃ = a₁ + (3 - 1) × d = 7 + 2 × 4 = 7 + 8 = 15

This matches our previous calculation, confirming that 15 is indeed the correct missing term.

Frequently Asked Questions

What is the difference between an arithmetic sequence and a geometric sequence?: An arithmetic sequence has a constant difference between terms, while a geometric sequence has a constant ratio between terms. For example, 2, 4, 8, 16 is a geometric sequence with a common ratio of 2.
Can I find the missing term if I don't know the first term?: Yes, you can find the missing term if you know any two terms and their positions in the sequence. You can rearrange the nth term formula to solve for the first term if needed.
What if the common difference is negative?: If the common difference is negative, the sequence will be decreasing. For example, 10, 7, 4, 1 has a common difference of -3. The formula still applies the same way.
Can this calculator handle sequences with fractions or decimals?: Yes, the calculator can handle sequences with any real numbers, including fractions and decimals. Just enter the values as you would normally.
What if I have more than one missing term in the sequence?: If you have more than one missing term, you'll need additional information to solve the sequence. Typically, you would need at least two known terms to determine the common difference and then use that to find the missing terms.