Question

The sum of first $n$ terms of an A.P is $5n-n^2$. Find the $n$th term of this A.P

• A. $6-5n$
• B. $6-2n$
• C. $5-2n$
• D. None of these

Answer 1

Answer: (B)

$6-2n$

Given,

$S_n=5n-n^2$

$S_1=a_1=5\left(1\right)-1^2=4$

$S_2=5\left(2\right)-2^2=6$

$a_2=S_2-a_1=6-4=2$

$d=a_2-a_1=2-4=-2$

$a_n=a+(n-1)d$

$a_n=4+(n-1)(-2)$

$\therefore a_n=6-2n$