Question

The 11^th term of an AP is 90 less than the first term. If the second term is 99, find the third term.
1. 108
2. 99
3. 90
4. 81

Answer 1

Correct Answer - Option 3 : 90

Given:

The 11th term of an AP is 90 less than the first term. The second term is 99.

Formula:

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’.

T₂ = a + d = 99              ----(1)

According to question

T₁ - T₁₁ = 90

⇒ a - (a + 10d) = 90

⇒ - 10d = 90

d = - 9

From equation (1)

a + (- 9) = 99

⇒ a = 108

Third term T₃ = a + 2d

⇒ 108 + 2 × - 9 = 108 - 18 = 90

∴ Required answer is 90.