Carrying Out the Plan

Applying the generalized solution

In the previous lesson, we considered and solved only the specific problem at hand. Now, let’s apply the generalized formula of the arithmetic series to solve both the problems that we looked at in the previous lessons.

Gauss’s problem

In this case, we have a sequence of numbers from 1 to 100. The first term of the sequence is 1, and the last term is 100. The total numbers in the sequence are 100. Now, let’s use this information to find the sum:

$$\begin{align*} \text{Sum} &= \frac{\text{100}}{2}\times(1 + 100) \\ &= 50\times 101 \\ &= 5050 \\ \end{align*}$$ ...