EM-1592

Number patterns and the nth term

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

A sequence is defined by

S_1 = 3^2 + 1^2 = 10

S_2 = 7^2 + 2^2 = 53

S_3 = 11^2 + 3^2 = 130

S_4 = 15^2 + 4^2 = 241

.

(a) Evaluate

S_5

.

(b) Hence find an expression for

S_n

in the form

an^2 + bn + c

, where

a, b

and

c

are integers.
What is the value of

a

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