Question

make three different patterns and formula the general rule for them.


please tell me the answer step by step​

Answer 1

Answer:

Let's call the position of a number in a term \(n\), so that we can use it to describe the value of the term. We call \(n\) a variable, as it can represent different values.

A general formula for any term in the sequence in the table is \((\text{10}n) - \text{5}\).

(Remember that \(\text{10} \times n\) can also be written as \(\text{10}n\).)

So for the 100th term in this sequence, \(n = \text{100}\) and the value of the term is \((\text{10} \times \text{100}) - \text{5} = \text{995}\).

What if you wrote a different number sentence for the pattern? You might have written:

\(\text{5} + [(\)\(\text{1}\)\(- \text{1}) \times \text{10}] = \text{5} + \text{0} = \text{5}\)

\(\text{5} + [(\)\(\text{2}\)\(- \text{1}) \times \text{10}] = \text{5} + \text{10} = \text{15}\)

\(\text{5} + [(\)\(\text{3}\)\(- \text{1}) \times \text{10}] = \text{5} + \text{20} = \text{25}\)

If you replace the number in bold by \(n\), you will get

\(\text{5} + [(n - \text{1}) \times \text{10}]\). You will find that this simplifies as follows:

\(\text{5} + [(n - \text{1}) \times \text{10}]\)

\(= \text{5} + \text{10}n - \text{10}\)