55. FORMULATES THE RULE IN FINDING THE NTH TERM USING DIFFERENT STRATEGIES �M6AL-IIID-7

ANNALICE R. QUINAY

Master Teacher 1

DRILL: SKIP COUNTING

Have the pupils skip count by 4, by 6, by 7 and by 9.

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PRESENT THE FF. SEQUENCES AND LET THE PUPILS GIVE THE 7^TH TERM IN EACH.

• 1.)5,12,19,26, …….
• 2.)2,10,18,26, ……
• 3. )2,10,50,250,……
• 4. )305,296,287,278, ……
• 5. )6,21,36,51, ………..

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GROUP ACTIVITY!

4, 10, 16, 22, 28

Write down the next two terms of the sequence.�b) Write down an expression for the n^th term of this sequence.�c) Work out the 50^th term of the sequence.

Solution: 4, 10, 16, 22, 28

a) From looking at the sequence we can see that each term is 6 larger than the previous term. We say the term-to-term rule is "add 6". Therefore the next two terms are 34 and 40.�b) The n^th term of a sequence is always written in the form "?n + ?".�The number in front of the "n" is always the difference to get from one term to the next. Since the difference is 6, the first part of our rule will be "6n". The rule follows the six times table: 6, 12, 18, 24... etc.

Now compare the 6 times table with our rule:������

�The numbers in the sequence are always 2 less than the 6 times table so we "adjust" our rule by subtracting 2. Now putting this together gives us: n^th term = 6n - 2.

c) Now we know the n^th term = 6n - 2 we just need to substitute n = 50 in order to find the 50^thterm of the sequence.�So: The 50^th term = 6 x 50 - 2�                        = 300 – 2 = 298

SHOW A VIDEO ON HOW TO FORMULATE THE RULE IN FINDING THE NTH TERM USING DIFFERENT STRATEGIES.�“WRITING A FORMULA FROM A SEQUENCE”

GROUP ACTIVITY:

PAIR-SHARE:

GROUP ACTIVITY: FINDING THE NTH TERM. �IN EACH QUESTION THERE ARE FOUR TERMS OF A SEQUENCE OF NUMBERS: �A) WRITE DOWN THE RULE USING N TO REPRESENT THE NTH TERM. �B) FIND THE 10TH AND 15TH TERMS.

Group Activity: Distribute this activity sheet to each group:

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ANSWERS:

HOW DO WE FIND / FORMULATE THE RULES IN FINDING THE NEXT TERM IN A SEQUENCE?

• Determine the order of numbers if it is ascending or descending.
• Find the difference between the consecutive terms.
• To find the rule of the next term, use the difference between terms.
• Example:

WRITE DOWN THE NEXT TERM FOR EACH OF THE FF. SEQUENCES, THEN FIND THE RULE.

A) WRITE DOWN THE RULE USING N TO REPRESENT THE NTH TERM. �B) FIND THE 30TH TERMS.

Study the following sequence of figure. Then, draw the next figure and write the rule used to find the answer.

ANNALICE R. QUINAY

Master Teacher 1