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GCSE Mathematics/Quadratic Equations
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2
: 3 : 10 : 23
1 7 13 first difference
6 6 second difference
using the formula
2a= the second difference
2a= 6
a=3
From finding a, you then proceed to find b
3a+b=first difference
3(3)+b=1
9+b=1
b=-8
Finding c
a+b+c= first term
3+(-8)+c=2
-5+c=2
c=7
Substitute the values for a, b and c into
Tn=an*2+bn+c (the first n being to the power of 2)
Tn= 3n*2-8n+7