(continuation of Lesson 3) WEEK 1 – LESSON 4 SEQUENCES nth TERM (continuation of Lesson 3) Angel G. Bassig

OBJECTIVE To be able to find the nth term of a sequence.

tn= 2n 2, 4, 6, 8, 10,………………..? Linear Number Sequences/Patterns The difference between adjacent terms is 2. 2 2 2 2 difference  1st 2nd 3rd 4th 5th................................nth position  2, 4, 6, 8, 10,………………..? terms  + 2 n 2n 1 2 4 3 6 8 5 10 Can you see how the numbers of this sequence are related to those in the 2 times table? tn= 2n

tn= 3n + 2 5, 8, 11, 14, 17,………………..? Linear Number Sequences/Patterns The difference between adjacent terms is 3. 3 3 3 3 difference  1st 2nd 3rd 4th 5th................................nth position  5, 8, 11, 14, 17,………………..? terms  + 2 n 3n 1 3 2 6 9 4 12 5 15 5 8 11 14 17 ? 3n + 2 Can you see how the numbers of this sequence are related to those in the 3 times table? tn= 3n + 2

5, 8, 11, 14, 17,…..? 1st 2nd 3rd 4th 5th.........nth 3 3 3 3 tn= 3n + 2 + 2 3, 7, 11, 15, 19,…..? tn= 4n - 1 - 1 4 4 4 4 n 4n 1 4 2 8 3 12 16 5 20 3 7 11 15 19 ? 4n - 1

5, 8, 11, 14, 17,…..? 1st 2nd 3rd 4th 5th.........nth 3 3 3 3 3, 7, 11, 15, 19,…..? 4 4 4 4 tn= 3n + 2 tn= 4n - 1 + 2 - 1 8, 13, 18, 23, 28,…..? tn= 5n + 3 5 5 5 5 + 3 n 5n 1 5 2 10 3 15 4 20 25 8 13 18 23 28 ? 5n + 3

tn= 3n + 2 tn= 4n - 1 tn= 5n + 3 tn= 2n - 3 5, 8, 11, 14, 17,…..? 5, 8, 11, 14, 17,…..? 1st 2nd 3rd 4th 5th.........nth 3 3 3 3 3, 7, 11, 15, 19,…..? 4 4 4 4 tn= 3n + 2 tn= 4n - 1 8, 13, 18, 23, 28,…..? 5 5 5 5 tn= 5n + 3 + 2 - 1 + 3 -1, 1, 3, 5, 7,…..? tn= 2n - 3 - 3 2 2 2 2 1. The common difference tells you the multiple of n required for the first part of the rule. 2. The second part of the rule is obtained by subtracting the first term and the common difference. 2a. This is equivalent to asking yourself what you need to do to the common difference to get to the value of the first term.

Example Question 1 For the number sequence below: (a) Find the “position to term” rule (b) Use your rule to find the 58th term (t58) Difference 7  7n 7  2  - 5 2, 9, 16, 23, 30,…… (a) tn= 7n - 5 (b) t58= 7 x 58 - 5 = 401 Example Question 2 For the number sequence below: (a) Find the “position to term” rule (b) Use your rule to find the 75th term (t75) 9, 15, 21, 27, 33,…… Difference 6  6n 6  9  + 3 (a) tn= 6n + 3 (b) t75= 6 x 75 + 3 = 453

Answer the following worksheets (2 worksheets) in pairs Let’s check your understanding … Answer the following worksheets (2 worksheets) in pairs Time: 10 Minutes

Find the nth term of: 3, 5, 7, 9, 11, … 2n + 1 4, 9, 14, 19, 24, … 6, 9, 12, 15, 18, … 1, 5, 9, 13, 17, … 3, 7, 11, 15, 19, … 8, 14, 20, 26, 32, … 4, 10, 16, 22, 28, … 13, 16, 19, 22, 25, … 0, 1, 2, 3, 4, 5, … 2n + 1 5n - 1 3n + 3 4n - 3 4n - 1 6n + 2 6n - 2 3n + 10 n - 1

Find the nth term of: 1, 3, 5, 7, 9, … 2n - 1 3, 8, 13, 18, 23, … 5, 8, 11, 14, 17, … 0, 4, 8, 12, 16, … 2, 6, 10, 14, 18, … 7, 13, 19, 25, 31, … 3, 9, 15, 21, 27, … 12, 15, 18, 21, 24, … 0, 2, 4, 6, 8, 10, … 2n - 1 5n - 2 3n + 2 4n - 4 4n - 2 6n + 1 6n - 3 3n + 9 2n - 2

Answer the following worksheets (2 worksheets) individually Let’s check your understanding … Answer the following worksheets (2 worksheets) individually Time: 10 Minutes

Find the nth term of: 4, 6, 8, 10, 12, … 2n + 2 5, 10, 15, 20, 25, … 7, 10, 13, 16, 19, … 2, 6, 10, 14, 18, … 4, 8, 12, 16, 20, … 5, 11, 17, 23, 29, … 9, 15, 21, 27, 33, … 14, 17, 20, 23, 26, … 0, 3, 6, 9, 12, 15, … 2n + 2 5n 3n + 4 4n - 2 4n 6n - 1 6n + 3 3n + 11 3n - 3

Find the nth term of: 4, 6, 8, 10, 12, … 2n + 2 5, 10, 15, 20, 25, … 7, 10, 13, 16, 19, … 2, 6, 10, 14, 18, … -4, 0, 4, 8, 12, … 15, 12, 9, 6, 3, … 1.5, 2, 2.5, 3, 3.5, … -2, -5, -8, -11, -14, … -3, 0, 3, 6, 9 … 17, 14, 11, 8, 5, … 2n + 2 5n 3n + 4 4n - 2 4n - 8 -3n + 18 ½n + 1 -3n + 1 3n – 6 -3n + 20

PLENARY Discuss the worksheet answers . Share one or two things learned in today’s lesson.