Which term of the A.P. 3, 10, 17, 24, ... will be 84 more than its 13t

1.	Which term of the A.P. 3, 10, 17, 24, ... will be 84 more than its 13th term ?
Answer» Given: 3, 10, 17, 24, ... First we need to calculate 13^th term. We know that a_n = a + (n – 1)d Here, a = 3, d = 10 – 3 = 7 and n = 13 So, a₁₃ = 3 + (13 – 1)7 ⇒ a₁₃ = 3 + 12 × 7 ⇒ a₁₃ = 3 + 84 ⇒ a₁₃ = 87 Now, the term is 84 more than a₁₃ is 84 + 87 = 171 Now, a + (n – 1)d = 171 ⇒ 3 + (n – 1)7 = 171 ⇒ 3 + 7n – 7 = 171 ⇒ 7n = 171 + 7 – 3 ⇒ 7n = 175 ⇒ n = 25 Hence, the 25^th term is 84 more than the 13^th term.

Which term of the A.P. 3, 10, 17, 24, ... will be 84 more than its 13th term ?

Answer»

Given: 3, 10, 17, 24, ...

First we need to calculate 13^th term.

We know that

a_n = a + (n – 1)d

Here, a = 3, d = 10 – 3 = 7 and n = 13

So, a₁₃ = 3 + (13 – 1)7

⇒ a₁₃ = 3 + 12 × 7

⇒ a₁₃ = 3 + 84

⇒ a₁₃ = 87

Now, the term is 84 more than a₁₃ is 84 + 87 = 171

Now,

a + (n – 1)d = 171

⇒ 3 + (n – 1)7 = 171

⇒ 3 + 7n – 7 = 171

⇒ 7n = 171 + 7 – 3

⇒ 7n = 175

⇒ n = 25

Hence, the 25^th term is 84 more than the 13^th term.