M3.8.8 For the adult
Sequences and the nth term
A dot pattern has 5, 8, 11 and 14 dots in its first four pictures. How many dots will the 100th picture have?
What this chapter teaches
When a sequence goes up by the same step each time, the nth term starts with that step times n. Compare with the sequence to find the number to add. The nth term then gives any term, such as the 100th, at once.
Three questions to ask
There is no one right wording. Listen for the idea.
- What does the sequence 5, 8, 11, 14 go up by each time?
- How do you find the 100th term without writing all of them?
- How can you test your nth term on the first two terms?
After the chapter, the learner can
- Find the nth term of a sequence like 5, 8, 11, 14
- Use the nth term to find the 100th term
What they copy into their notebook
Find the common difference. It is the number in front of n. Compare with that many n, and add what is left. Then put in n = 100 to jump far ahead.