Question:
The fifth term of an AP of \(n\) terms, whose sum is \(n^2 – 2n\), is:
\(n\) पदों की AP का 5वाँ पद, जिसका योग \(n^2 – 2n\) है, है:
Options:
- 5
- 7
- 8
- 15
- 5
- 7
- 8
- 15
Correct Answer: b)
Explanation:
The sum of \(n\) terms is \(S_n = n^2 – 2n\).
The \(n^{\text{th}}\) term is \(T_n = S_n – S_{n-1}\).
For \(n = 5\):
\[S_5 = 5^2 – 2(5) = 25 – 10 = 15\]
\[S_4 = 4^2 – 2(4) = 16 – 8 = 8\]
Therefore, the 5th term is:
\[T_5 = S_5 – S_4 = 15 – 8 = 7\]
Hence, the correct option is (b).
\(n\) पदों का योग \(S_n = n^2 – 2n\) है।
\(n\)वाँ पद: \(T_n = S_n – S_{n-1}\)।
\(n = 5\) के लिए:
\[S_5 = 5^2 – 2(5) = 15\]
\[S_4 = 4^2 – 2(4) = 8\]
अतः 5वाँ पद:
\[T_5 = S_5 – S_4 = 15 – 8 = 7\]
अतः सही विकल्प (b) है।