"Sequence" worksheet for Micro-teaching!

Sequence worksheet

We have a sequence such as: 3, 7, 11, 15,19,23,27...

Part (l): Sequence Terms:


1. What is the first term? _____
2. What is the second term? _____
3. What is the difference between first and second term? _____
4. Now what is the third term? _____

A.Finding difference “d”:

1. What is the difference between second and third term? _____
2. What is difference between any consecutive numbers in the sequence? _____
Call this “d”.
3. Thus d = _____


Part (II): Relationship between each term!


Each number in the sequence is called a “term” and they are indicated as “tn”; for instance, t1 is first term, t2 is the second term, t3 is third term and so on. Now please note that 3+4=7

1. What is 3 in terms of “term”? t? _____
2. What is 7 in terms of “term”? t? _____
3. What is the relationship between t1 and t2?
4. Yes that's right t1 +d= t2
5. Now what is the relationship between t2 and t3? _____
6. What is the relationship between t4 and t3? _____

Part (III): Finding the nth term in the sequence/final formula:


A.Writing each term in terms of t1 and d:

Back to part (II) questions 4 and 5, we found out that

a) t1 +d= t2
b) t2 +d= t3

Now, using a) and b) above, we can write t3 in terms of t1 and d
(Hint: substitute t1 +d= t2 into t2 +d= t3)
t2 +d= t3 and since t1 +d= t2 ------ t1 +d+d= t3 -----
t1 +2d= t3


1.Now using the result above try to write t4 in terms of t1 and d (hint: write t4 in terms of t3 and substitute the above result for t3 and simply the work) what do you get?




2.Again using the result above do the same thing for t5, what do you get?






B.Finding n th term using general formula:

1.Writing each terms in terms of t1 and d using the same method that was shown above we see a trend! By looking at the above examples that we did you notice any trend for writing tn in terms of t1 and d?


The above question leads us to the general formula for finding nth term in the sequence. For instance in our sequence that we had in part (I) by using the general formula we can easily find 5th, 6th term, ……, 100th term and so on.

2.Now using the general formula found above, can you find the 20th and 10th term of the sequence?