Linear sequences A linear sequence is a list

Linear sequences A linear sequence is a list of numbers that have a common difference between each number in the list. Finding the rule that can extend the sequence from the previous term is called the term to term rule. This is a basic requirement of sequences but we need to extend our knowledge.

Write down the rule and fill in the spaces. 1. 4 10 16 2. 2 3. 5 5 3. 32 25 18 22 6. 5 11 28 …… …… ……

Position to term rules It is important to be able to find the number in a sequence from its position in that sequence. Example. If we want to find the 100 th term in the sequence 2, 6, 10, 14, 18……… Do we need to keep adding 4, until we find the 100 th number in the sequence!! Any suggestions?

1, 2, 3, 4, 5 ………………. Position in sequence (n) 2, 6, 10, 14, 18 ………………. Common difference = 4 4, 8, 12, 16, 20………………. Numbers in 4 x table (4 n) To find numbers in sequence multiply position by 4 and take 2 nth Term = 4 n – 2 100 th term = (4 x 100) – 2 = 398

1, 2, 3, 4, 5 ………………. Position in sequence (n) 8, 13, 18, 23, 28 ………………. Common difference = 5 5, 10, 15, 20, 25………………. Numbers in 5 x table (5 n) To find numbers in sequence multiply position by 5 and add 3 nth Term = 5 n + 3 100 th term = (5 x 100) + 3 = 503

For each of the number sequences below, find a rule for the nth term (tn) and work out the value of t 100. Question 1 8, 13, 18, 23, 28, tn= 5 n + 3 Question 2 1, 4, 7, 10, 13, tn= 3 n - 2 t 100= 3 x 100 - 2 = 298 Question 3 2, 9, 16, 23, 30, tn= 7 n - 5 t 100= 7 x 100 - 5 = 695 Question 4 9, 15, 21, 27, 33, tn= 6 n + 3 t 100= 6 x 100 + 3 = 603 Question 5 -1, 4, 9, 14, 19, tn= 5 n - 6 t 100= 5 x 100 - 6 = 494 Question 6 -3, 1, 5, 9, 13, tn= 4 n - 7 t 100= 4 x 100 - 7 = 393 Question 7 6, 18, 30, 42, 54, tn= 12 n - 6 t 100= 5 x 100 + 3 = 503 t 100= 12 x 100 - 6 = 1194

Using an nth term to generate a sequence 29 October 2021 If an nth term is given, it is possible to work out any value in the sequence. It is likely that a question may ask you to generate the first five terms of a sequence from an nth term. Example Find the first five terms of the sequence from the following nth terms. 1. 4 n + 2 6, 10, 14, 18, 22 2. 7 n – 4 3, 10, 17, 24, 31 3. 12 n – 5 7, 19, 31, 43, 55