Math Problem Statement
If the 1st number in a series of consecutive odd numbers is 8 less than the last number in the series. How many numbers are there in the series?
Solution
Let the series of consecutive odd numbers be . The first number is and the last number is the -th term, which is .
According to the problem, the first number is 8 less than the last number, so we have the equation:
Now, solve for :
Subtract from both sides:
Add 2 to both sides:
Now divide by 2:
Thus, there are 5 numbers in the series.
Would you like more details or have any questions? Here are 5 related questions to further explore the topic:
- How would the series change if the difference were more than 8?
- What happens if the series includes both even and odd numbers?
- Can you find the sum of the numbers in this series?
- What would happen if the series consisted of consecutive even numbers instead?
- How would the solution change if the series started with a specific number?
Tip: When dealing with arithmetic sequences, always focus on the relationship between the first and last terms to set up equations easily.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Arithmetic Sequences
Formulas
nth-term formula for an arithmetic sequence: a_n = a_1 + (n-1)d
Equation based on problem condition: x + 8 = x + 2(n-1)
Theorems
Arithmetic Sequence Formula
Suitable Grade Level
Grades 6-8