Question

Find the sum of the following AP $1,3,5,\mathrm{7.............199}$

Answer 1

AP is $1,3,5,\mathrm{7....}199$

$a=1,d=2$ and last term $l=199$

$t_n=a+(n-1)d\Rightarrow 199=1+(n-1)\times 2\Rightarrow 2n=200n=100\therefore sum=\frac{n}{2}[a+l]=\frac{100}{2}[1+199]=\frac{100}{2}\times 200=10000$