What is the sum of 25 + 26 + 27 + ......... + 189 ?
Monday, March 30, 2015
[Pri20150303VSA] A way to Visualise Arithmetic Progressions
This is a problem meant to stretch the minds of
school pupils. Adults (e.g. parents,
teachers and tutors) trying to help out usually recommend doing this using the “rainbow” method (where a bunch of arcs
are drawn joining 25 and 189, 26 and 188, 27 and 187 ... and so on, forming
something that looks like rainbow), or the sum
of arithmetic progression formula Singapore
½ ´ number of terms ´ (first term + last term)
which is usually taught at the junior college (pre-university) level. Although correct, do the learners understand the logic behind them?
A Visual Method
In my visual representation below, the answer pops out almost immediately and the reasoning is made apparent to the student.