The sequence is 10,13,18,25,34
Now work out the difference between the terms
13–10 , 18–13, 25–18, 34–25
3, 5, 7, 9
Now work out the difference between these terms
5–3,7–5,9–7
2,2,2
Because the secondary difference is a constant, we know that the sequence is a polynomial of degree 2 (a quadratic)
A quadratic is in the form y=ax^2+bx+c
substitute our values of ‘x’ and ‘y’.
We only need to use the first 3 values
x=1 y=10
x=2 y=13
x=3 y=18
substitute into the quadratic equation
10=a+b+c
13=4a+2b+c
18=9a+3b+c
solve simultaneously.
I will use matrices
therefore the sequence equation is y=x^2+9
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