The tutor introduces a typical arithmetic series example.

An arithmetic series is a sum of numbers which change by repeated addition. An example:

5+11+17+23+….+143

The question posed might be as follows:

Find the sum of the arithmetic series 5+11+17+23+….+143.

Solution:

A formula for the sum is

S_n=n(t₁+t_n)/2

where

t₁ is the first term

t_n is the last term

n is the number of terms.

Note that while, in our case, t₁=5 and t_n=143, we don’t yet know n.

However, we can use the term formula

t_n=t₁+d(n-1)

in which d is the amount added to get the next term; in our case, d=6.

We can find n as follows:

143=5+6(n-1)

which becomes

138=6(n-1)

Next, dividing both sides by 6, we get

23=n-1

n=24

Apparently 143 is the 24th term. Now, to find the sum of 5+11+17+23+….+143, we can use

S_n=n(t₁+t_n)/2

as follows:

S₂₄=24(5+143)/2=24(148)/2=12(148)=1776

Apparently, 5+11+17+23+….+143=1776:)

Source:

Travers, Kenneth J. et al. Using Advanced Algebra. Toronto: Doubleday Canada, 1977.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.