Question

In an AP: 

Given a = 5, d = 3, a_n = 50. find n and S_n.

Answer 1

Given : 

a = 5; d = 3; 

a_n = a + (n – 1)d = 50 

⇒ 50 = 5 + (n – 1) 3 

⇒ 50 – 5 = 3n – 3 

⇒ 3n = 45 + 3

⇒ n = 48/3 = 16 

Now, S_n = \(\frac{n}{2}\)(a + l) 

S₁₆ = \(\frac{16}{2}\)(5 + 50) 

= 38 × 55 

= 440