nth_term_algebra_level_6

Slide 1:

A few sequences… 9, 13, 17, 21…. ….. 25, 29 term to term rule: add 4

Slide 2:

A few sequences… 20, 15, 10, 5…. ….. 0, -5 term to term rule: minus 5

Slide 3:

A few sequences… 1, 10, 100, 1000…. ….. 10,000, 100,000 term to term rule: x 10

Slide 4:

A few sequences… 88, 44, 22, 11…. ….. 5.5 , 2.75 term to term rule: half

Slide 5:

10, 20, 30, 40, 50, 60, 70…… 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th The position to term rule is: whichever term I’m interested in X 10

Slide 6:

4, 8, 12, 16, 20, 24, 28…… 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th The position to term rule is: whichever term I’m interested in X 4 n nth term = n x 4

Slide 7:

What is the position to term rule: 2, 4, 6, 8, 10 …. nth term = 6, 12, 18, 24 …. nth term = 6n 5, 10, 15, 20, 25…. nth term = 5n 100, 200, 300, 400…. nth term = 100n What’s the 7 th term? What’s the 10 th term? What’s the 18 th term? n x 2 = 2n 700 1000 1,800

Slide 8:

more complicated…. 5, 8, 11, 14, 17, 20 ….. +3 +3 +3 +3 +3 common difference is 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 nth term = 3n + 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 + 2

Slide 9:

6, 11, 16, 21, 26… Step 1: Common difference? nth term = 5n Step 2: How has the table been shifted? + 1 To work out the rule for the nth term of a sequence 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 + 1

Slide 10:

Questions to try: Work out the rule for the nth term then work out the 100 th term 3, 5, 7, 9, 11, 13…. 12, 20, 28, 36, 44…. 19, 29, 39, 49, 59…. 7, 10, 13, 16, 19…. 14, 20, 26, 32, 38…. 55, 60, 65, 70, 75 … 8, 17, 26, 35, 44 …. !! Extension: 1, 9, 17, 25, 33…. -2, 8, 18, 28, 38…. -2, -4, -6, -8, -10 … 1, 4, 9, 16, 25…. 3, 6, 11, 18, 27…. !!

Slide 11:

You own a taxi company that charges as follows: £3.50 for calling the cab 20p for every minute of journey time Real Life Example: Work out a formula for the cost of a journey that’s n minutes long Use your formula to cost a journey of 2 hours

Slide 12:

What pattern of matchsticks would follow this sequence rule: 4n + 2

Extension work:

Extension work T( n ) = n 2 T( n ) = 3n 2 + n T( n ) = 4n 2 + n – 1 For each of these sequences work out the first five terms What is the first difference? What is the second difference? Is there a way of predicting the second difference?