Us to represent the pattern T_n = 2n + 1 in three equivalent forms: verbally, in a flow diagram, and by a number sentence.

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

5. Equivalent forms

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------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- The problem asks us to represent the pattern $T_n = 2n + 1$ in three equivalent forms: verbally, in a flow diagram, and by a number sentence.

a) Verbally
This form describes the pattern using words.
The pattern starts with the first term $T_1 = 2(1) + 1 = 3$.
The common difference is $d=2$, which means each subsequent term is found by adding 2 to the previous term.
Alternatively, we can describe the rule $T_n = 2n + 1$ directly.

The verbal representation is:
To find any term in the pattern, multiply the term number by 2 and then add 1.
The pattern starts with 3, and each subsequent term is obtained by adding 2 to the previous term.

b) In a flow diagram
A flow diagram illustrates the sequence of operations to transform the input (term number, $n$) into the output (term value, $T_n$).

The flow diagram is:
Input (Term number, $n$) $\rightarrow$ [Multiply by 2] $\rightarrow$ [Add 1] $\rightarrow$ Output (Term, $T_n$)

c) By a number sentence
A number sentence is the algebraic rule or formula that defines the pattern. This was already determined in the previous question.

The number sentence for the pattern is:

$$T_n = 2n + 1$$

Here is the completed table:

| Equivalent Form | Representation | | :---------------- | 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