How do you find the rule for this sequence:
3, 5,7,9,11,13...
What do you think?
The rule for this sequence is by 2 because it starts by 3 plus 2 equals 5 and that's the next number 5.
To find the rule for this sequence, you need to identify the pattern or relationship between the numbers. In this case, you can observe that the sequence is increasing by 2 each time.
Here's how you can explain it step by step:
1. Look for differences between consecutive terms:
- The difference between the second term (5) and the first term (3) is 2.
- The difference between the third term (7) and the second term (5) is 2.
- The difference between the fourth term (9) and the third term (7) is 2.
- The pattern continues, and the difference remains constant.
2. Write down the increment:
- From step 1, we found that the numbers in the sequence are increasing by 2 each time.
3. Identify the initial term:
- The first term in the sequence is 3.
4. Write the rule:
- By combining the increment and the initial term, we can describe the rule for this sequence as "start with 3 and increase by 2 each time."
Therefore, the rule for this sequence is: An = 3 + (n - 1) * 2, where An represents the nth term of the sequence.