Question

In the sequence an= 7n+1, what is the domain value (n) if the range is 29?

Answer 1

We can see that we have the following sequence:

`a_n=7n+1`

And we need to find the value of the domain, n, for which the value of the range is equal to 29.

1. We already know that the range of a sequence, roughly speaking, consists of the terms the sequence that the sequence can take after following the rule for the sequence and taking into account the values of the domain. The domain of a sequence is the natural numbers 1, 2, 3, and so on.

2. Then we can pose the situation as follows:

`29=7n+1\text{ \lparen The value of the range for the value n is 29\rparen}`

3. Now, to find the value of n, we have, first, to subtract 1 from both sides of the equation, and then divide both sides by 7:

`\begin{gathered} 29-1=7n+1-1 \\ \\ 28=7n \\ \\ (28)/(7)=(7n)/(7) \\ \\ 4=n \\ \\ n=4 \end{gathered}`

Therefore, the domain value, n, if the value of the range is 29 is n = 4 (first option).