Notes by Shibili Prasanth Science Grinds Junior Cert Maths HL Notes by Shibili Prasanth Science Grinds

NOTES: NTH TERM Sequence – An ordered list of numbers Term – A number in a sequence Term position (n) – Place of term in sequence 2, 5, 8, 11, 14, ___ Term Position 1 2 3 4 5 6 Term Sequence

Learning objectives: To find the next terms in a sequence and to find the nth term of a sequence

4n + 2 1st term = 4 × 1 + 2 = 6 2nd term = 4 × 2 + 2 = 10 3rd term = 4 × 1 + 2 = 6 2nd term = 4 × 2 + 2 = 10 3rd term = 4 × 3 + 2 = 14 4th term = 4 × 4 + 2 = 18 5th term = 4 × 5 + 2 = 22 6 10 14 18 22

5n - 4 1st term = 5 × 1 - 4 = 1 2nd term = 5 × 2 - 4 = 6 = 5 × 3 - 4 = 5 × 1 - 4 = 1 2nd term = 5 × 2 - 4 = 6 = 5 × 3 - 4 3rd term = 11 4th term = 5 × 4 - 4 = 16 5th term = 5 × 5 - 4 = 21 1 6 11 16 21

Write the first five terms of these sequences 9 11 13 15 9 14 19 24 14 20 26 32 5 9 13 17 19 27 35 43 13 22 31 40 14 21 28 35 -1 2 5 8 11

4 8 12 16 20 24 28 3 7 11 15 19 23 27 4 4 4 4 4 4 4n -1

7 14 21 28 35 42 49 1 8 15 22 29 36 43 7 7 7 7 7 7 7n -6

5, 7, 9, 11… 2n + 3 3n + 3 6, 9, 12, 15… 4n - 3 1, 5, 9, 13… 3n + 2 5, 8, 11, 14… -4n + 16 12, 8, 4, 0…

NOTES: NTH TERM To write the rule of the sequence: Find the amount the pattern is changing by. Write that number in front of X. Ask yourself what do you have to do to that number to get your first term. EX: 5,9,13,17 It is changing by 4 so write 4x. Then ask how you get from 4 to 5, which is add 1, so the rule is 4x+1. To find the nth term: Plug the number in for x and solve. EX: What is the 9th term in the sequence 2x -7 You would have 2(9)-7 which is 11, so your answer is 11.

Finding nth term Which rule shows the relationship between a term and n, its position in the sequence? 2n 4n n2 n3 2(3) = 6 X Position Term 1 4 2 8 3 12 16 n 20 4(3) = 12 X (3)2 = 9 (3)3 = 27 X

Plug in the top, see if you get the bottom! Finding nth term 1 2 3 4 5 6) Match the sequence to its expression: 4, 5, 6, 7, 8, … Choices A. n + 5 B. 4n C. 2n + 2 D. n + 3 X 3 + 5 = 8 X 4(3) = 12 Plug in the top, see if you get the bottom! X 2(3) + 2 = 8 3 + 3 = 6

Finding nth term Which sequence follows the rule n2 + 4, where n represents the position of a term in the sequence? 6, 8, 10, 12, 14, … 5, 8, 11, 14, 17, … 6, 10, 14, 18, 22, … 5, 8, 13, 20, 29 Position 1 2 3 4 5 Term 12+4 =5 22+4 =8 32+4 =13 42+4 =20 52+4 =29

Plug in the top, see if you get the bottom! Finding nth term 1 2 3 4 5 6) Match the sequence the expression: 0, 7, 14, 21, 28, … Choices A. 7n + 7 B. n + 7 C. 7n – 7 D. n - 7 X 7(2) + 7 = 28 X (2) + 7= 9 Plug in the top, see if you get the bottom! 7(2) – 7 = 7 X (2) – 7 = -5