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GB-21-04-001 · Quadratic nth term

Find an expression for the nth term of the quadratic sequence.
30,64,104,150,20230,\quad 64,\quad 104,\quad 150,\quad 202

Sequences: Quadratic nth Term Booklet p. 26
Method
1) Find 1st and 2nd differences
2) a = 2nd difference ÷ 2
3) Draw table (n², sequence, an², subtract)
4) Find linear nth term of bottom row
Worked Example (GB-21-04-001)
1) 1st diffs: +34,  +40,  +46+34,\; +40,\; +46 \quad 2nd diff =+6  ⇒  a=6÷2=3= \color{#dc2626}{+6} \;\Rightarrow\; a = 6 \div 2 = \mathbf{3}
nn11223344Rule
n2n^21144991616
Sequence30306464104104150150
3n23n^233121227274848⇒3n2\Rightarrow \mathbf{3n^2}
Subtract (Seq−3n2\text{Seq} - 3n^2)272752527777102102⇒+25n+2\Rightarrow \mathbf{+25n + 2}
3n2+25n+23n^{2} + 25n + 2