Question

For a sequence of natural numbers find ∑n=201∑1n=20

Answer 1

We know the sum of $n$ terms of an A.P with first term $a$ and the common difference $d$ is:

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

Here, it is given that the first term is $a=1$, common difference is $d=2-1=1$ and $n=20$, therefore, the sum is:

$S_{20}=\frac{20}{2}\left[\right(2\times 1)+(20-1\left)\right(1\left)\right]=10(2+19)=10\times 21=210$

Hence, the sum is $210$.