Sum of n term, Sn = 2n² - 3n

Sum of (n - 1) terms, S(n-1)

= 2(n - 1)² - 3(n - 1)
= 2(n² - 2n + 1) - 3n + 3
= 2n² - 4n + 2 - 3n + 3
= 2n² - 7n + 5


The nth term, Tn

= Sn - S(n - 1)
= 2n² - 3n - (2n² - 7n + 5)
= 2n² - 3n - 2n² + 7n - 5
= 4n - 5


So the (n - 1)th term, T(n-1)

= 4(n - 1) - 5
= 4n - 4 - 5
= 4n - 9


Tn - T(n - 1)

= 4n - 5 - (4n - 9)
= 4n - 5 - 4n + 9
= 4


This is the difference between any two consecutive terms and since it is a constant 4, it is a common difference and so the sequence is an arithmetic progression

Sn > 350


2n² - 3n > 350

2n² - 3n - 350 > 0

(2n + 25)(n - 14) > 0

Divide by 2 ,

(n + 12.5)(n - 14) > 0

(Either use cross factor method or mentally)

Positive coefficient of n means the quadratic graph is upward sloping (u-shaped)


n < -12.5 (rejected as n cannot be 0 or negative) or n > 14


Least n = 15