--DEFINITIONS--
"What is the nth term of a sequence?"
"The nth term" of a sequence is a formula that lets you find any term in a sequence of numbers directly without listing all the previous terms.
"What is a term of a sequence?"
For example, in the sequence 3, 5, 7, 9, 11, … the 'First term' refers to 3... the 'Second term' refers to 5... and so on...
"What is a linear sequence?"
"The nth term of a linear sequence comes in the form of 'an + b' (e.g. 3x + 2), /or/ (nth term = (common difference) × n + (shift) which means the common difference between each number in the sequence is always the same digit."
For example, in the sequence 4, 7, 10, 13… we can see that the common difference is always the number '3'.
"Now let's see how this works step-by-step!"
--WORKED EXAMPLE--
Let's use this sequence: 4, 7, 10, 13
Step 1: Identify the common difference
In this case 4, 7, 10, 13 the common difference is...
'+3'
Step 2: Find the nth terms multiple
In this case as the common difference is 3, the nth term multiple is 3, giving '3n'
Step 3: Find the shift
To find the shift, we compare the sequence to the times table of the common difference and find the difference. In this case our sequence is: 4, 7, 10, 13, and the 3 times table is: 3, 6, 9, 12.
"So what’s the difference?"
4 − 3 = 1, 7 - 6 = 1, 10 - 9 = 1, 13 - 12 = 1
So the "Shift" is '+1'
...the nth term is '3n + 1'
TASK:
You will be assigned a question to work through step-by-step and post your process on the Padlet below. You may use the example given as a guide on how to structure your answer.
--WORKSHEETS--