The 6th and 17th terms of an A.P. are 19 and 41 respectively, find t

1.	The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
Answer» Given, a₆ = 19 and a₁₇ = 41 We know that, n^th term a_n = a + (n – 1)d So, a₆ = a + (6-1)d ⇒ a + 5d = 19 …… (i) Similarity, a₁₇ = a + (17 – 1)d ⇒ a + 16d = 41 …… (ii) Solving (i) and (ii), (ii) – (i) ⇒ a + 16d – (a + 5d) = 41 – 19 11d = 22 ⇒ d = 2 Using d in (i), we get a + 5(2) = 19 a = 19 – 10 = 9 Now, the 40^th term is given by a₄₀ = 9 + (40 – 1)2 = 9 + 78 = 87 Therefore the 40^th term is 87.

The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.

Answer»

Given,

a₆ = 19 and a₁₇ = 41

We know that, n^th term a_n = a + (n – 1)d

So,

a₆ = a + (6-1)d

⇒ a + 5d = 19 …… (i)

Similarity,

a₁₇ = a + (17 – 1)d

⇒ a + 16d = 41 …… (ii)

Solving (i) and (ii),

(ii) – (i) ⇒

a + 16d – (a + 5d) = 41 – 19

11d = 22

⇒ d = 2

Using d in (i), we get

a + 5(2) = 19

a = 19 – 10 = 9

Now, the 40^th term is given by a₄₀ = 9 + (40 – 1)2 = 9 + 78 = 87

Therefore the 40^th term is 87.