EM-1594

Number patterns and the nth term

E Math · Secondary 4 · Hard · Number patterns and the nth term

A sequence has first four terms

U_1 = 3^2 + 1^2 = 10

U_2 = 7^2 + 2^2 = 53

U_3 = 11^2 + 3^2 = 130

U_4 = 15^2 + 4^2 = 241

.
Find a formula for

U_n

in the form

an^2 + bn + c

, where

a, b

and

c

are integers.

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