Question

The 6^th term of an AP is 99. If the 1^st term increase by 1 and the common difference decrease by 2 then the 6^th term so obtained would be equal to the 5^th term of the original AP. Find the 3^rd term of this AP.
1. 69
2. 72
3. 75
4. 77

Answer 1

Correct Answer - Option 2 : 72

Given:

The 6^th term of an AP is 99. If the 1^st term increases by 1 and the common difference decrease by 2 then the 6^th term so obtained would be equal to the 5^th term of the original AP.

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’.

From the question

T₆ = 99

⇒ a + 5d = 99     ----(1)

After increasing ‘a’ by 1 and decreasing‘d’ by 2 we get,

6^th term of New AP = 5^th term of original AP

⇒ (a + 1) + 5 × (d - 2) = a + 4d

⇒ a + 5d - 9 = a + 4d

⇒ d = 9

After putting value of ‘d’ in equation (1) we get,

a = 54

Third term of AP = a + 2d

⇒ 54 + 2 × 9 = 54 + 18 = 72

∴ required answer is 72.