Question

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

Answer 1

A.P. is 3, 10, 17, ..........

Here, a = 3, d – 10 – 3 = 7

T₁₃ = a + 12d

= 3 + 12 × 7

= 3 + 84

= 87

Let n^th term is 84 more then its 13^th term

∴ T_n = 84 + 87 = 171

`\implies` a + (n – 1)d = 171

`\implies` 3 + (n – 1) × 7 = 171

`\implies` (n – 1) × 7 = 171 – 3 = 168

`\implies` n – 1 = `(168)/(7)` = 24

`\implies` n = 24 + 1

`\implies` n = 25

∴ 25^th term is the required term.