Enter the count of consecutive numbers and their average to quickly calculate the sequence. This tool supports sequences of consecutive integers, odd numbers, and even numbers.
Given \( n \) consecutive numbers with an average \( A \), follow these steps to determine the sequence:
1. Calculate the Total Sum:
\( S = A \times n \).
2. Determine the First Term:
- For Consecutive Integers: Using the sum formula for an arithmetic sequence: \( S = \frac{n}{2} \times (2a + n - 1) \) Solve for \( a \): \( a = \frac{S - \frac{n(n - 1)}{2}}{n} \)
- For Consecutive Odd or Even Numbers: With a common difference of 2, the sum formula becomes: \( S = \frac{n}{2} \times (2a + (n - 1) \times 2) \) Solve for \( a \): \( a = \frac{S - n(n - 1)}{n} \)
3. Build the Sequence:
Use the first term \( a \) and the common difference to generate the full sequence.
Solution:
1. Calculate the total sum:
\( S = 97 \times 5 = 485 \)
2. Determine the first term:
\( a = \frac{485 - \frac{5 \times 4}{2}}{5} = \frac{485 - 10}{5} = 95 \)
3. Build the sequence:
95, 96, 97, 98, 99
Result: The consecutive integers are 95, 96, 97, 98, 99.
Solution:
1. Calculate the total sum:
\( S = 61 \times 5 = 305 \)
2. Determine the first term:
\( a = \frac{305 - 5 \times 4}{5} = \frac{305 - 20}{5} = 57 \)
3. Build the sequence:
57, 59, 61, 63, 65
Result: The consecutive odd numbers are 57, 59, 61, 63, 65.