How do You Find the Nth Term in a Arithmetic Sequence

Assignment Task

Teacher A: Gets into class and explains to learners how to find the nth term.

Whenever we have a pattern given to you pictorially:

First, you have to generate numbers that go along with it.

Secondly, you check the differences between consecutive terms until the differences remain

The same. This will tell you whether we have a linear, quadratic or cubic pattern.
Thirdly, find the nth term by using the relevant general terms of the sequence/pattern Now consider the following example.

Therefore, this is a linear pattern because the constant difference is found at the first level. The general term is Tn = a + (n-1)d = 3 + 2(n-1) = 2n2+3=2n+1

That is, the nth term is 2n + 1

Now, find the number of dots in the nth shape of the following pattern

Teacher B: Gets into class and distribute sheets with the following activity and ask learners to work on that in their groups. During the discussions she goes to different
groups checking their work and assisting where necessary.
Use the given pattern hereunder to respond to the accompanying questions.

• Use at least three ways to describe how the pattern is growing.
• Use each of your intepretations to construct the fifth shape.
• Use each a rule to explain the number of light squares in the sixth diagram.
• Write down the expression or formula for the number of squares in Diagram.
• Which diagram will have a total of 144 shaded squares?

Write a 4 page essay in which you compare and contrast the two teaching episodes. Your essay should address, but not limited to, the following:

• The teacher's views of mathematical knowledge
•  How mathematical knowledge is acquired?

This Mathematics has been solved by our PHD Experts at My Uni Papers.