Question

1.) Write a sequence with at least 5 terms that forms a pattern . Identify the rule.2.) The first term in a sequence is an odd number. The rule is to multiply by 2 . Explain why the rest of the terms in sequence will be even numbers.

Answer 1

1. Increases by 5 units

2. Any odd number multiplied by an even one yields an even number.

1) We can write out a sequence, an arithmetic one, to follow a pattern.

`5,10,15,20,25,\ldots`

Note that the pattern here is the common difference between each term the first one is 5 and all the other ones increase by 5 units.

2) In this second case, we can pick "5" as well, but in this one, we'll make a Geometric Sequence for the following numbers will be written as the product of the prior term times 2:

`5,10,20,40,\ldots`

Note that all the terms will be even numbers because any odd number multiplied by an even one yields another even number.