Question

Find the sum of all odd numbers from $5$ to $205$

Answer 1

It is an A.P with $a=5$ ,$d=2$ and $a_n=205$

where

a=first term

d=common difference

therefore,

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

substituting value

$205=5+(n-1)2$

$(n-1)2=200$

$n-1=100$

$n=101$

Now,

Sum pf numbers in sequence$=\frac{n}{2}[2a+(n-1\left)d\right]$

$=\frac{101}{2}[2\times 5+(101-1)\times 2]$

$=10605$

Therefore the sum of all odd numbers from $5$ to $205$ is $10605$.