Question

The sum of the first $n$ terms of an A.P is $4n^2+2n$. Find the $n$th term of this A.P.

• A. $5n-2$
• B. $8n-2$
  
• C. $3n-2$
• D. None of these

Answer 1

The correct option is B $8n-2$

Given,

$S_n=4n^2+2n$

$S_1=a_1=4(1{)}^2+2(1)=6$

$S_2=4(2{)}^2+2(2)=20$

$a_2=S_2-a_1=20-6=14$

$d=a_2-a_1=14-6=8$

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

$a_n=6+(n-1)8$

$\therefore a_n=8n-2$