Problem
ALG-B1-M05-P008 Constant Second Differences
#8
★★☆☆☆ Level 2 of 5
The sequence \(a_n\) begins \(2,5,10,17,26\). Suppose the second differences are constant. Find a formula for \(a_n\).
First differences are \(3,5,7,9\).
The differences are \(2n+1\) from \(a_n\) to \(a_{n+1}\). This corresponds to \(a_n=n^2+1\). Check: \(1^2+1=2\), \(2^2+1=5\), and so on.
First entry into finite differences.