Question

If the sum of the first n terms of an A.P. is 4n-n^2, What is the first term? What is the sum of first two terms? What is the second term? Similarly, find the third, the tenth and the nth terms.

Answer 1

$S_{(}n)=4n-n^2$

$\therefore S_1=a_1=4\left(1\right)-(1{)}^2=3$

$S_2=a_2=4\left(2\right)-(2{)}^2=4$

$S_3=a_3=4\left(3\right)-(3{)}^2=3$

$\therefore a_2=S_2-S_1=4-3=1$

$a_3=S_3-S_2=3-4=-1$

Common difference,

$d=a_2-a_1=1-3=-2$

$\therefore a_n=a_1+(n-1)d$

$=3+(n-1)(-2)$

$=5-2_n$

$\therefore a_{1}0=5+(n-1)d$

$=5-20$

$=-15$