19 15.5 12 Find The Nth Term Calculator

How to Use This Calculator

To use the 19 15.5 12 find the nth term calculator:

1. Enter the first term of the sequence in the first input field.
2. Enter the second term of the sequence in the second input field.
3. Enter the third term of the sequence in the third input field.
4. Enter the position (n) of the term you want to find in the fourth input field.
5. Click the "Calculate" button to see the result.
6. Review the result and the sequence chart showing the pattern.

The calculator will display the nth term of the arithmetic sequence based on the three provided terms.

The Formula Explained

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This difference is called the common difference (d).

The general formula for the nth term of an arithmetic sequence is:

Where:

• aₙ is the nth term
• a₁ is the first term
• d is the common difference
• n is the term number

To find the common difference (d) from three terms, we use:

Once we have the common difference, we can find any term in the sequence using the general formula.

Worked Examples

Example 1: Finding the 5th Term

Given the sequence terms: 19, 15.5, 12

1. First term (a₁) = 19
2. Second term (a₂) = 15.5
3. Third term (a₃) = 12
4. Find the common difference (d):
• d = a₂ - a₁ = 15.5 - 19 = -3.5
• Verify with a₃: d = a₃ - a₂ = 12 - 15.5 = -3.5
5. Find the 5th term (a₅):
• a₅ = a₁ + (5 - 1) × d = 19 + 4 × (-3.5) = 19 - 14 = 5

The 5th term of the sequence is 5.

Example 2: Finding the 10th Term

Given the sequence terms: 19, 15.5, 12

1. First term (a₁) = 19
2. Second term (a₂) = 15.5
3. Third term (a₃) = 12
4. Find the common difference (d):
• d = a₂ - a₁ = 15.5 - 19 = -3.5
• Verify with a₃: d = a₃ - a₂ = 12 - 15.5 = -3.5
5. Find the 10th term (a₁₀):
• a₁₀ = a₁ + (10 - 1) × d = 19 + 9 × (-3.5) = 19 - 31.5 = -12.5

The 10th term of the sequence is -12.5.