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##### Investigative Skills Toolkit

Use the TI-Nspire Handheld (either Numeric or CAS) to investigate and generalise results from numerical patterns.

Author: Nevil Hopley

Topic: Mathematics

Tags Patterns , Scattergraphs , Linear regression , Modelling

*There are two versions of this activity - one for Numeric Nspire users and one for Computer Algebra System (CAS) Nspire users. They cover the same core material, whilst the CAS worksheets use the full algebra functionality of that handheld.*

The TI-Nspire and mathematical skills that will be developed are:

- defining functions;
- using sigma notation;
- generating sequences;
- using statistical regression models to reveal algebraic generalisations.

**Mathematical Aim**

As a context for developing the above four skills, the students will use them to find the algebraic formula for the sum:

1 + 2 + 3 + 4 + .... +n

They will then find the algebraic formula for the sum:

1² + 2² + 3² + 4² + .... +n²

and finally the formula for:

1³ + 2³ + 3 ³+ 4³ + .... +n³

Note: There are many ways to derive the formula for these sequence sums, and some are quicker than the approach followed in this activity. However, an important purpose of this task is to experience how a wide variety of technological skills can be brought together to work in powerful ways. Such techniques can then be used even when the formulae being sought are not as well known as the above three sequence sums.

Structure of Tasks

Tasks 1, 2, 3 and 4 introduce each of the 4 individual skills, listed above.

Task 5 merges these skills together in order to achieve the mathematical aim given above.