How do you find the 20th number in a series?

To find the 20th number in an arithmetic sequence, you need to know the first term and the common difference between terms. Here's how you do it:

According to the YouTube video, "Find the 20th Term of the Arithmetic Sequence 4, 11, 18, 25," the following approach is recommended:

Understanding Arithmetic Sequences

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant. This constant difference is called the "common difference."

• First Term (a): The first number in the sequence.
• Common Difference (d): The constant amount added to get to the next term.

Formula for the nth term

The formula to find the nth term (in this case, the 20th term) of an arithmetic sequence is:

a_n = a + (n - 1)d

Where:

• a_n is the nth term
• a is the first term
• n is the term number (20 in this case)
• d is the common difference

How to find the 20th number

1. Identify the first term (a): Look at the sequence and note the first number.
2. Calculate the common difference (d): Subtract any term from the term that follows it.
3. Apply the formula:
   • Substitute n = 20, the first term, and the common difference into the formula.
   • Calculate the result.

Example

Let's use the sequence from the YouTube video: 4, 11, 18, 25...

1. First Term (a): 4
2. Common Difference (d): 11 - 4 = 7
3. Apply the formula:
   • a₂₀ = 4 + (20 - 1) * 7
   • a₂₀ = 4 + 19 * 7
   • a₂₀ = 4 + 133
   • a₂₀ = 137

Therefore, the 20th number in the sequence 4, 11, 18, 25... is 137.

Key Takeaway

To find the 20th term, or any term in an arithmetic sequence, you start with the first term and add the common difference multiplied by one less than the term number you are looking for. As the reference highlights, you add the common difference 19 times to the first term to get the 20th term.