Question

Given a = 7, a₁₃ = 35, find d and S₁₃.

Answer 1

Given: a = 7; 

a₁₃ = a + 12d = 35 

⇒ 7 + 12d = 35 

⇒ 12d = 35 – 7 

⇒ n = \(\frac{28}{12}\) = \(\frac{7}{3}\)

Now, S_n = \(\frac{n}{2}\)(a + l) 

S₁₃ = \(\frac{13}{2}\)(7 + 35) 

= \(\frac{13}{2}\) × 42 

= 13 × 21 

= 273