Question

If the sum of first n terms of an A.P is $4n-n^2.$ what is the first term? what is the sum of first two terms Also find 2nd,3rd,10th and nth terms of A.P.

Answer 1

Let $a$ is first term and $d$ is common difference $\frac{n}{2}(2a+(n-1\left)d\right)=4n-n^2$

$an+\frac{n(n-1)d}{2}=4n-n^2$

$a=3andd=-2$

Sum of first $2$ terms $=4\times 2-2^2=4$

$2^{nd}$ term $=3+(2-1)\times -2=1$

$3^{rd}$ term $=3+(3-1)\times -2=-1$

${10}^{th}$ term $=3+(10-1)\times -2=-15$

$n^{th}$ term $=3+(n-1)\times -2=5-2n$