Question

The 21^st term of an AP is 172. The 12^th term of the AP is 16 less than the 14^th term. Find the second term.
1. 16
2. 21
3. 18
4. 20

Answer 1

Correct Answer - Option 4 : 20

Given:

The 21st term of an AP is 172. The 12th term of the AP is 16 less than the 14th term.

Formula used:

nth term of an AP, T_n = a + (n - 1)d, where ‘a’ is the first term, ‘n’ is the total number of terms and ‘d’ is the common difference.

Calculation:

Let the first term is ‘a’ and common difference is‘d’.

T₂₁ = a + 20d = 172       ----(1)

According to question

T₁₄ – T₁₂ = 16

⇒ (a + 13d) - (a + 11d) = 16

⇒ 2d = 16

⇒ d = 8

And from equation (1)

a = 12

Second term T₂ = a + d

⇒ 12 + 8 = 20

∴ Required answer is 20.