alleryIf the sum of the first $n$ terms of an AP is $S_n=4n-n^2$, what is the $n$th term of the AP?
A$5-2n$
B$4-n$
C$3-2n$
D$5-n$
Answer & Solution
Correct answer: A. $5-2n$
The $n$th term is $a_n=S_n-S_{n-1}$. Here,
$$S_{n-1}=4(n-1)-(n-1)^2=4n-4-(n^2-2n+1)= -n^2+6n-5.$$
So
$$a_n=(4n-n^2)-(-n^2+6n-5)=5-2n.$$
Hence the $n$th term is $5-2n$.
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