Problem
ALG-B1-M05-P004 Squares from a Recurrence
#4
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The sequence is defined by \(a_1=1\), \(a_{n+1}=a_n+2n+1\). Find \(a_{20}\).
Prove that \(a_n=n^2\).
By induction, \(a_n=n^2\). Hence \(a_{20}=400\).
Difference of consecutive squares.