The sum of the first 6 terms of an arithmetic progression is 0 and its 4th term is 2. If the sum of its first n terms is 1440, then the value of n is: 

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AAI Junior Assistant (Fire Service) Official Paper (Held On: 15 Nov 2022 Shift 1)
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  1. 36
  2. 30
  3. 28
  4. 32

Answer (Detailed Solution Below)

Option 2 : 30
Free
ST 1: English
20 Qs. 20 Marks 25 Mins

Detailed Solution

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Given:

The sum of the first 6 terms of an arithmetic progression is 0 and its 4th term is 2. If the sum of its first n terms is 1440.

Formula used:

Sum of first n terms of an AP:

nth term of an AP:

Calculation:

Given sum of first 6 terms:

Given 4th term:

Solving these two equations:

From

⇒ 

Substitute in 

⇒  ⇒ d = 4

Substitute d back in 

⇒  ⇒ 

Given sum of first n terms is 1440:

⇒ 

⇒ 

⇒ 

⇒ 

⇒ n(n - 30) + 24(n - 30) = 0

⇒ (n - 30) (n + 24) = 0

⇒ n = 30 or -24

Since n must be positive:

∴ The correct answer is option (2).

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