for a patterned sequence and use it to generate terms in that sequence Good morning! L.O. Find the nth term rule for a patterned sequence and use it to generate terms in that sequence Level 6

By the end of today’s lesson: All of you will be able to identify the next term in a patterned sequence. (Level 5) 2) Most of you will be able to find the nth term rule and use it to find a term in an ascending sequence. (Level 6) 3) Some of you will be able to find the nth term and use it to find a term in a descending sequence. (Level 6)

Farmer Barleymow

14m

1m 1m section of fence 2m section of fence Task: Draw the pattern for a 3m section of fence and count how many pieces of wood are used 1m section of fence 2m section of fence

3m section of fence 10m of wood How much wood for 14m of fencing?

n 1 2 3 4 4 7 10 13 3n 3 6 9 12 + 3 3n + 1 3 times tables! Wood Pattern n Pattern number 1 2 3 4 4 7 10 +3 13 Wood +1 3n 3 6 9 12 What else goes up in 3s ?? + 3 term-to-term rule: 3n + 1 nth term rule: How much wood for 14m of fencing? 3 times tables!

Pattern n 1 2 3 4 4 7 10 13 Wood 3n + 1 nth term rule: n=14 Task: Use the nth term rule to calculate how many pieces of wood are needed for a 14m section of fence 3n+1 = (3x14)+1= =43

I need a taller fence!!

1m 2m Task: Draw the pattern for a 3m section of fence and count how many pieces of wood are used

n 1 2 3 7 12 17 nth term rule 5n +2 Rule is 5n+2 3m section Task: Calculate the nth term rule for this sequence and use to work out how much wood is needed for a 14m section of fencing Rule is 5n+2 3m section For 14m fence, 17 pieces of wood (5x14)+2= =72 Wood Pattern n 1 2 3 -5 7 +5 12 +5 17 nth term rule 5n +2

Matchstick Patterns 1 2 3 4 6 11 16 21 - 5 1 +5 +5 +5 Rule is 5n + 1 Number of huts (n) 1 2 3 4 Matches 6 11 16 21 - 5 1 +5 +5 +5 Rule is 5n + 1

Number of matches = 5n + 1 How many matches need for 50 huts? Matches = (5 x 50) + 1 = 251

n Descending SEQUENCES 1 2 3 4 5 12, 9, 6, 3, 0 . . . Task: Work out the nth term rule and write down the value of the 100th term in the sequence. Descending SEQUENCES n 1 2 3 4 5 - 3 - 3 12, 9, 6, 3, 0 . . .

Rule is -3n+15 For 100th term, (-3x100)+15 = =-285 - -3 =? n 1 2 3 4 5 - -3 - 3 - 3 12, 9, 6, 3, 0 . . . nth term rule -3n +15

Find the nth term rule and use it to work out how many matches are needed for the 50th pattern in these sequences: 6n-2 1. nth term rule Matches in 50th pattern 298 Number of matches 4 10 16 3n+1 2. nth term rule Number of matches 4 7 10 Matches in 50th pattern 151 3. 2n+1 nth term rule Number of matches 3 5 7 Matches in 50th pattern 101 17/01/2019 L.O. Find the nth term rule for a patterned sequence and use it to generate terms in that sequence (Level 6)

4. nth term rule 3n Matches in 50th pattern 150 Number of matches 3 6 9 12 5. nth term rule 8n-4 Matches in 50th pattern Number of matches 4 396 12 20 6. nth term rule 7n+1 Number of matches 8 15 22 Matches in 50th pattern 351 7. nth term rule Number of connecting rods in each shape 4n+1 5 9 13 rods in 25th pattern 101

Find the nth term rule and use it to work out how many matches are needed for the 50th pattern in these sequences: 1. nth term rule Name: Matches in 50th pattern Number of matches 2. nth term rule Number of matches Matches in 50th pattern 3. nth term rule Number of matches Matches in 50th pattern 17/01/2019 L.O. Find the nth term rule for a patterned sequence and use it to generate terms in that sequence (Level 6)

4. 5. 6. 7. nth term rule Matches in 50th pattern Number of matches connecting rods in each shape lines in 25th pattern

By the end of today’s lesson: All of you will be able to identify the next term in a patterned sequence. (Level 5) 2) Most of you will be able to find the nth term rule and use it to find a term in an ascending sequence. (Level 6) 3) Some of you will be able to find the nth term and use it to find a term in a descending sequence. (Level 6)