How To Find Missing Term In Arithmetic Sequence?

How to Find the Missing Term in an Arithmetic Sequence

Have you ever been given a math problem with a missing term in an arithmetic sequence? Maybe you were asked to find the 10th term of a sequence that starts with 2 and increases by 3 each term. Or perhaps you were given a list of numbers and asked to find the missing number, such as 2, 5, 8, ?, 14.

Finding the missing term in an arithmetic sequence is a relatively simple task, as long as you know the formula. In this article, we will discuss what an arithmetic sequence is, how to find the missing term, and provide some examples.

What is an Arithmetic Sequence?

An arithmetic sequence is a list of numbers in which each term is the sum of the previous term and a constant difference. The constant difference is also known as the common difference.

For example, the following is an arithmetic sequence:

2, 5, 8, 11, 14, …

The common difference in this sequence is 3, because each term is 3 more than the previous term.

How to Find the Missing Term

To find the missing term in an arithmetic sequence, you can use the following formula:

Tn = a + (n – 1)d

where:

  • Tn is the missing term
  • a is the first term in the sequence
  • n is the position of the missing term
  • d is the common difference

For example, let’s say we want to find the missing term in the following sequence:

2, 5, 8, ?, 14, …

The first term is 2, the common difference is 3, and the missing term is in the fourth position. So, we can use the formula to find the missing term:

T4 = 2 + (4 – 1)3 = 11

Therefore, the missing term is 11.

Step Formula Example
Find the common difference (d) d = a2 – a1 d = 10 – 5 = 5
Find the number of terms (n) n = (tn – a1) / d n = (40 – 5) / 5 = 8
Find the missing term (tn) tn = a1 + (n – 1)d tn = 5 + (8 – 1)5 = 40

An arithmetic sequence is a sequence of numbers in which each term is the sum of the previous term and a constant, called the common difference. The general formula for an arithmetic sequence is:

$a_n = a_1 + (n-1)d$

where:

  • $a_n$ is the nth term of the sequence
  • $a_1$ is the first term of the sequence
  • $d$ is the common difference

For example, the sequence 1, 4, 7, 10, 13, … is an arithmetic sequence with a common difference of 3.

How to Find the Missing Term in an Arithmetic Sequence?

There are two ways to find the missing term in an arithmetic sequence:

1. Using the formula
2. Using a table

Using the formula

To use the formula, substitute the known terms into the general formula and solve for the missing term. For example, to find the missing term in the sequence 1, 4, 7, 10, 13, …, we would substitute 1 for $a_1$, 5 for $n$, and 3 for $d$ into the formula:

$a_n = a_1 + (n-1)d$

$a_5 = 1 + (5-1)3 = 16$

Therefore, the missing term is 16.

Using a table

To use a table, create a table of the terms of the sequence, starting with the first term and ending with the term after the missing term. The missing term will be the number that lies in the middle of the table. For example, to find the missing term in the sequence 1, 4, 7, 10, 13, …, we would create the following table:

| Term | Value |
|—|—|
| 1 | 1 |
| 2 | 4 |
| 3 | 7 |
| 4 | 10 |
| 5 | 13 |
| 6 | 16 |

The missing term is 16, which is the number that lies in the middle of the table.

Finding the missing term in an arithmetic sequence is a simple task that can be done using either the formula or a table. The formula is more efficient if you only need to find one missing term, while the table is more efficient if you need to find multiple missing terms.

How To Find Missing Term In Arithmetic Sequence?

An arithmetic sequence is a sequence of numbers in which each term is the sum of the previous term and a constant, called the common difference. The general formula for an arithmetic sequence is:

$$a_n = a_1 + (n-1)d$$

where:

  • $a_n$ is the nth term of the sequence
  • $a_1$ is the first term of the sequence
  • $d$ is the common difference

To find the missing term in an arithmetic sequence, we can use the following methods:

  • The formula method
  • The table method
  • The graph method

The Formula Method

The formula method is the most straightforward way to find the missing term in an arithmetic sequence. To use this method, simply substitute the known values of $a_1$, $n$, and $d$ into the formula above and solve for $a_n$.

For example, let’s say we want to find the missing term in the arithmetic sequence 2, 5, 8, 11, …?. We know that the first term is 2, the common difference is 3, and we want to find the fifth term. Substituting these values into the formula, we get:

$$a_5 = 2 + (5-1)3 = 16$$

Therefore, the missing term is 16.

The Table Method

The table method is another way to find the missing term in an arithmetic sequence. To use this method, simply create a table of the terms of the sequence. The first row of the table should list the terms of the sequence, and the second row should list the differences between the terms.

For example, let’s say we want to find the missing term in the arithmetic sequence 2, 5, 8, 11, …?. We would create a table like this:

| Term | Number | Difference |
|—|—|—|
| 1 | 2 | – |
| 2 | 5 | 3 |
| 3 | 8 | 3 |
| 4 | 11 | 3 |
| 5 | ? | 3 |

Now, we can see that the missing term is 16. This is because it is the number that lies in the middle of the table.

The Graph Method

The graph method is a third way to find the missing term in an arithmetic sequence. To use this method, simply graph the terms of the sequence. The missing term will be the point on the graph that lies halfway between the two known terms.

For example, let’s say we want to find the missing term in the arithmetic sequence 2, 5, 8, 11, …?. We would graph the terms of the sequence like this:

![Graph of an arithmetic sequence](https://upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Arithmetic_sequence_graph.svg/300px-Arithmetic_sequence_graph.svg.png)

We can see that the missing term is 16. This is because it is the point on the graph that lies halfway between the two known terms, 8 and 11.

In this article, we have discussed three methods for finding the missing term in an arithmetic sequence. The formula method is the most straightforward, while the table method and graph method are more visual. You can use whichever method you prefer, depending on your own learning style.

How to Find Missing Term in Arithmetic Sequence?

Q: What is an arithmetic sequence?

A: An arithmetic sequence is a sequence of numbers in which each term is the sum of the previous term and a constant, called the common difference. For example, the sequence 1, 3, 5, 7, 9 is an arithmetic sequence with a common difference of 2.

Q: How do I find the missing term in an arithmetic sequence?

A: There are several ways to find the missing term in an arithmetic sequence. One way is to use the following formula:

tn = a1 + (n – 1)d

where:

  • `tn` is the nth term in the sequence
  • `a1` is the first term in the sequence
  • `n` is the number of terms in the sequence
  • `d` is the common difference

For example, to find the missing term in the sequence 1, 3, 5, 7, 9, we would use the following formula:

t5 = 1 + (5 – 1)2 = 11

Another way to find the missing term in an arithmetic sequence is to use a graph. To do this, plot the terms of the sequence on a graph. The missing term will be the point on the graph that lies directly in between two known terms.

Q: What are some common applications of arithmetic sequences?

A: Arithmetic sequences are used in a variety of applications, including:

  • Finance: The interest on a loan or investment is often calculated using an arithmetic sequence.
  • Physics: The motion of a projectile is often described using an arithmetic sequence.
  • Biology: The growth of a population of organisms is often described using an arithmetic sequence.

Q: What are some tips for finding the missing term in an arithmetic sequence?

A: Here are some tips for finding the missing term in an arithmetic sequence:

  • Make sure you understand the definition of an arithmetic sequence.
  • Identify the common difference in the sequence.
  • Use the formula or a graph to find the missing term.
  • Check your answer to make sure it is correct.

Q: What are some common mistakes people make when finding the missing term in an arithmetic sequence?

A: Here are some common mistakes people make when finding the missing term in an arithmetic sequence:

  • Not understanding the definition of an arithmetic sequence.
  • Not identifying the common difference in the sequence.
  • Using the wrong formula or graph.
  • Not checking their answer to make sure it is correct.

Q: Where can I learn more about arithmetic sequences?

A: There are many resources available online and in libraries to learn more about arithmetic sequences. Here are a few suggestions:

  • [Khan Academy](https://www.khanacademy.org/math/algebra/sequences-and-series/arithmetic-sequences/a/arithmetic-sequences-)
  • [Math is Fun](https://www.mathsisfun.com/sequences/arithmetic-sequence.html)
  • [Encyclopedia of Math](https://www.encyclopediaofmath.org/index.php/Arithmetic_sequence)

    we have discussed how to find the missing term in an arithmetic sequence. We first reviewed the definition of an arithmetic sequence and the formula for finding the nth term. We then showed how to use this formula to find the missing term in a sequence given the first few terms. Finally, we presented two examples of how to find the missing term in a sequence.

We hope that this article has been helpful in understanding how to find the missing term in an arithmetic sequence. Remember, the key is to first identify the type of sequence you are working with and then apply the appropriate formula. With a little practice, you will be able to find the missing term in any arithmetic sequence.

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