We have a = 3

Then d = 5 – 3 = 2

Then, S_n = 288

We can recall that, S_n = × (2a + (n – 1)d)

So, S_n = × (2(3) + (n – 1)2)

⇒ S_n = × (6 + 2n – 2)

⇒ S_n = × (4 + 2n)

⇒ S_n = n × (2 + n)

⇒ S_n = n² + 2n

⇒ n² + 2n = 288

⇒ n² + 2n – 288 = 0

⇒ n² + 18n – 16n – 288 = 0

⇒ n(n + 18) – 16(n + 18) = 0

⇒ (n + 18)(n – 16)= 0

So we have n = – 18 or 16

But as n cannot be negative so, we have n = 16

∴ the correct option is (c)