--DEFINITIONS--
"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...
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"What is a term-to-term rule?"
It's an instruction that tells you how to get from one term to the next, for example, in the sequence 2, 5, 8, 11, 14, … The difference is clearly +3 each time; therefore, the 'term-to-term rule' is..
“Add 3 to the previous term.”
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"What is a linear sequence?"
"We learned the term 'linear' before, meaning 'straight line' with a 'constant slope,' so a 'LINEAR SEQUENCE' is a string of numbers that have a 'COMMON DIFFERENCE' between them. So, 2, 5, 8, 11, 14 is a linear sequence, as the common difference between each number is the same (+3)
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"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.
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"How to find the nth term of 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)
For example, in the sequence 2, 5, 8, 11, 14… we can see that the common difference is always the number '3'.
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"Now let's see how this works step-by-step!"
--WORKED EXAMPLE--
This example is the first sequence in the worksheet below.
Linear 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 find the difference between the times table of the common difference and our sequence. In this case our sequence is: 4, 7, 10, 13, and the times table of the common difference is the 3 times table which 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'
--WORKSHEETS--
"Complete these worksheets using the guidance below."
"Choose one of your completed sequences from the worksheets and show your process using the exact 4-step method you can see in my example below."