Question

Find the sum of the whole number from 1 to 560

Answer 1

The sum of whole numbers from 1 to 560 is an arithmetic series and as such, we will employ the formulae to solving the problem.

The sum of an arithmetic progression is given as:

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

Where:

n = total numbers summed = 560 in this case

a = 1st term = 1 in this case

d = common difference = 1

Substituting into the sum equation gives us:

$\begin{gathered} \frac{560}{2}(2(1)+(560-1)1) \\ 280(2+559) \\ 280(561)=157,080 \end{gathered}$

Find the sum of the whole number from 1 to 560 is 157,080

We can see that if we add either ends of the number series to each other, we get the value of

561 = (1+560), (2+559), (558+3).

Also we can see simply that these will go on about:

$\frac{560}{2}=280\text{ times}$

We, therefore, then multiply (280 x 561) = 157,080