Linear sequences are sequences that go up by a set amount each time.
For example 2 4 6 8 10 12 is a linear sequence of even numbers.
the diffrence between each number in the sequence is 2, so we call the nth term for this sequence 2n. So, now if we were asked to find the 5th term in the sequence we would do 2x5=10 TA DA! it works.
Now we have this sequence:
we add 3 each time... but this isn't the 3x tables? so if we just put 3n it wouldn't work! So we have to take 2 away from 3n to get it to the number we want. 3n-2.
Lets check this by finding the 5th term. 3x5=15 15-2= 13! It works!
When the diffrence between the terms changes we call it a quadratic sequence.
- If the second difference is 2, you start with n2
- If the second difference is 4, you start with 2n2
- If the second difference is 6, you start with 3n2
So, we add or minus a number to get it to the value we want, just like in linear sequences.
Practice Makes perfect!
try out this for quadratic sequences
And this for Linear: