choose the function that represents the triangular numbers.

$y = 0.5x + 0.5$
$y = 0.5^x + 0.5x$
$y = \frac{x}{0.5} + 0.5x$
$y = 0.5x^2 + 0.5x$

Question

choose the function that represents the triangular numbers.

$y = 0.5x + 0.5$
$y = 0.5^x + 0.5x$
$y = \frac{x}{0.5} + 0.5x$
$y = 0.5x^2 + 0.5x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangular Numbers" ], "new_concepts": [], "current_concepts": [ "Triangular Numbers" ] } ## Identify the values from the given pattern $$ \begin{aligned} &\text{For } x = 2, \quad y = 3 \ &\text{For } x = 3, \quad y = 6 \ &\text{For } x = 4, \quad y = 10 \ &\text{For } x = 5, \quad y = 15 \ &\text{For } x = 6, \quad y = 21 \end{aligned} $$ ## Test the given options using $x = 2$ $$ \begin{aligned} &\text{Option 1: } y = 0.5(2) + 0.5 = 1.5 eq 3 \ &\text{Option 2: } y = 0.5^2 + 0.5(2) = 0.25 + 1 = 1.25 eq 3 \ &\text{Option 3: } y = \frac{2}{0.5} + 0.5(2) = 4 + 1 = 5 eq 3 \ &\text{Option 4: } y = 0.5(2^2) + 0.5(2) = 2 + 1 = 3 \end{aligned} $$ ## Verify the correct option with $x = 3$ $$ y = 0.5(3^2) + 0.5(3) = 4.5 + 1.5 = 6 $$

$y = 0.5x + 0.5$

$y = 0.5^x + 0.5x$

$y = \frac{x}{0.5} + 0.5x$

$y = 0.5x^2 + 0.5x$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Triangular Numbers" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the values from the given pattern

Test the given options using \(x = 2\)

Verify the correct option with \(x = 3\)

Answer: