The first and the last terms of an A.P are 17 and 350 respectively. If

1.	The first and the last terms of an A.P are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
Answer» Given A.P in which a = 17 Last term = l = 350 Common difference, d = 9 We know that, a_n = a + (n – 1) d 350 = 17 + (n- 1) 9 ⇒ 350 = 17 + 9n – 9 ⇒ 9n = 350 – 8 ⇒ n = \(\frac{342}{9}\) = 38 Now, S_n = \(\frac{n}{2}\)(a + l) S₃₈ = \(\frac{38}{2}\)(17 + 350) = 19 × 367 = 6973 ∴ n = 38; S_n = 6973

The first and the last terms of an A.P are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Answer»

Given A.P in which a = 17

Last term = l = 350

Common difference, d = 9

We know that, a_n = a + (n – 1) d

350 = 17 + (n- 1) 9

⇒ 350 = 17 + 9n – 9

⇒ 9n = 350 – 8

⇒ n = \(\frac{342}{9}\) = 38

Now, S_n = \(\frac{n}{2}\)(a + l)

S₃₈ = \(\frac{38}{2}\)(17 + 350)

= 19 × 367 = 6973

∴ n = 38; S_n = 6973