Question
Download Solution PDFThe 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:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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
⇒
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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