If T_n = 6n + 5, find S_n

From the question we know that, T_n = 6n + 5 ……. (1)

And we know that T_n = a + (n – 1)d

So we have,

⇒ a + (n – 1)d = 6n + 5

⇒ a + (n – 1)d = 6n + 11 – 6

⇒ a + (n – 1)d = 11 + (6n – 6)

⇒ a + (n – 1)d = 11 + 6(n – 1)

On comparing both the sides, we have:

⇒ a = 11 and d = 6

So now, S_n = × (2a + (n – 1)d)

⇒ S_n = × (2(11) + (n – 1)(6))

⇒ S_n = × (22 + 6n – 6)

⇒ S_n = × (16 + 6n)

⇒ S_n = n × (8 + 3n)

⇒ S_n = 3n² + 8n

∴ Sum of n terms of the given A.P is S_n = 3n² + 8n