For AI agents: use /llms.txt for the Nakafa content index.
An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is always constant. This difference in an arithmetic sequence is denoted by .
Consider the following number sequence:
In this sequence, we can see that:
Since the difference between consecutive terms is always , this sequence is an arithmetic sequence with common difference .
The common difference () in an arithmetic sequence can be calculated by subtracting consecutive terms:
Where:
To determine the th term of an arithmetic sequence, we can use the formula:
Where:
If we write the first few terms of an arithmetic sequence:
From this pattern, we can see that the th term is:
Consider the number of seats in a performing arts theater:
To determine the number of seats in a specific row, we need to find the pattern in this data.
Step : Finding the common difference between rows
We can see that the difference between the number of seats in consecutive rows is . This means the number of seats in this theater forms an arithmetic sequence with:
Step : Using the formula to find the number of seats in row
Therefore, there are seats in row .
Given an arithmetic sequence with the rd term equal to and the th term equal to . Find the formula for the th term.
To determine the formula for the general term, we need to find the values of the first term and the common difference .
We eliminate these equations to find the value of :
After finding , we substitute it into the first equation to find :
With and , we can formulate the th term:
Therefore, the formula for the general term of this sequence is
Rudi saves money in a bank with a constant monthly increase. If in the th month, he saves and in the th month, Rudi saves .
What is the monthly increase in savings amount?
How much money did Rudi save for the first time?
Rudi's savings form an arithmetic sequence because the monthly increase is constant.
Finding the monthly increase in savings
Eliminating equations and :
Therefore, the monthly increase in Rudi's savings is .
Finding Rudi's initial savings
We have found , now we substitute it into equation to find :
Therefore, Rudi's initial savings was .
