If 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 $5-2n$.

Practise this question with Quill — AP Calculus AB →

Keep practising Unit 1A3: Function Composition and Inverses

Browse all Unit 1A3: Function Composition and Inverses questions for AP Calculus AB, or explore more Mathematics topics.

Start a Unit 1A3: Function Composition and Inverses lesson →