Problem
ALG-B1-M11-P014 Sequence
#14
★★★☆☆ Level 3 of 5
\(u_0=1\), \(u_{n+1}-u_n=2n+3\). Find \(u_n\).
Sum the differences.
\(u_n=1+\sum_{k=0}^{n-1}(2k+3)=1+n(n-1)+3n=n^2+2n+1=(n+1)^2\).
Strategy: telescoping differences.