**Mathematics 3** ESO – Unit 3 SEQUENCES page 27 activity 34

**a)** An arithmetic sequence is a sequence of numbers such that the difference of any two successive numbers of the sequence is a constant.

Watch the video on “Arithmetic sequences and series” and answer:

- I) What number is n
_{3}in the sequence? - II) What is “d”?
- III) What is the value of “d”?
- IV) Use the formula in the video to find a
_{50}(the 50^{th}term of the sequence). - V) What would be the value of a
_{50}if the difference was 6?

**b)** Watch the video on “Is A Number In A Sequence” and answer:

- I) Is “43” a term in the sequence “2n + 4”? Why?
- II) Is “95” a term in the sequence “3n – 1”? Why?

**c)** A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.

Watch the video on “Geometric sequences and series” and answer:

- I) What is a geometric sum?
- II) What three things do we need to know to solve a geometric sum?
- III) Using the formula, find S
_{8} - IV) Use the formula to find S
_{50}(the 50^{th}term of the sequence). - V) What would be the value of S
_{50}if the difference was 6?

**d)** Watch the video on “How to find the first four terms of a sequence” and answer:

- I) Why is the series an “alternate sign” series?
- II) Find a
_{12}