Describe the pattern T_n = 2n + 1 using verbal descriptions, a flow diagram, and a number sentence.

Here are the equivalent forms for the pattern $T_n = 2n + 1$.

5. Equivalent forms

a) Verbally
The pattern starts with 3, and each subsequent term is obtained by adding 2 to the previous term.
Alternatively, to find any term, multiply the term number by 2 and then add 1.

b) In a flow diagram
Input (Term number, $n$) $\rightarrow$ [Multiply by 2] $\rightarrow$ [Add 1] $\rightarrow$ Output (Term, $T_n$)

c) By a number sentence
The number sentence (or general rule) for the pattern is:

Here is the completed table:

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The pattern is "add 2 to the previous term".

a) Verbally
To find any term in the pattern, start with the number 3 and repeatedly add 2 to get the next term.
Alternatively, the rule is: two times the term number plus one.

b) In a flow diagram

[Start]
  |
  V
[Input: Term number (n)]
  |
  V
[Multiply by 2]
  |
  V
[Add 1]
  |
  V
[Output: Term (T_n)]
  |
  V
[End]

c) By a number sentence
The general rule for the pattern is: