Unit 5.1: Arithmetic Sequences

• Sequences and series is an exciting part of the curriculum. Make sure the learners know the difference between arithmetic and geometric sequences.
• If the sequence or series is arithmetic then:
• Expressing terms as follows is important for learners to understand:
• For arithmetic:

Arithmetic Series

When the terms of a sequence are added together, a series is formed.

A story of a historical even or of a contrived situation can motivate pupils. To introduce the sum of an arithmetic series, tell the story about young Carl Freidrich Gauss, who was in a class that was asked by the instructor to add the numbers from 1-100. Much to the astonishment of the instructor, young Guass who was aged 10 years, produced the correct answer immediately/ When asked how he arrived at the answer he quickly explained that:

1 + 100 = 101

2 + 99 = 101

3 + 98 = 101

Since there are 50 such pairs, the answer is 50 x 101 = 5050. This scheme can be used to develop the sum of an arithmetic series.

Proof for the sum of terms of arithmetic series(Examinable)

Activity

Note: fractions are shown as follows: 1/2, 2/3 etc.