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

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

Answer»

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

Discussion