What is the general nth term?

Why is the general term a quadratic expression?

The sequence follows the recurrence relation:

a_1 = 2

a_2 = a_1 + 3

a_3 = a_2 + 4

a_4 = a_3 + 5

a_n = a_(n-1) + (n+1)

= a_(n-2) + (n) + (n+1)

= a_(n-3) + (n-1) + (n) + (n+1) —- (involves a summation of ‘n’ terms of b_n = n+1)

= a_1 + 3 + 4 + …. + (n+1)

= 2 + (n-1)(n+4)/2

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