"What kind of sequence is this? 2, 10, 50, 250, ... Choices: [[arithmetic][geometric][both][neither]] "

Sequence Type Determination: To determine the type of sequence, we need to examine the relationship between consecutive terms. Let's check if it's an arithmetic sequence by finding the difference between consecutive terms. Difference between second and first term: 10 - 2 = 8 Difference between third and second term: 50 - 10 = 40 Difference between fourth and third term: 250 - 50 = 200Arithmetic Sequence Analysis: Since the differences between consecutive terms are not constant (8, 40, 200), the sequence is not arithmetic.Geometric Sequence Analysis: Now let's check if it's a geometric sequence by finding the ratio between consecutive terms. Ratio of second to first term: 10 / 2 = 5 Ratio of third to second term: 50 / 10 = 5 Ratio of fourth to third term: 250 / 50 = 5Since the ratio between consecutive terms is constant (5), the sequence is a geometric sequence.

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What kind of sequence is this? $2, 10, 50, 250, \ldots$ Choices:Choices: $\newline$ $\text{[A]arithmetic}$ $\newline$ $\text{[B]geometric}$ $\newline$ $\text{[C]both}$ $\newline$ $\text{[D]neither}$

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Algebra 2

Classify formulas and sequences

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Q. What kind of sequence is this?

2, 10, 50, 250, \ldots

Choices:Choices:

\newline

\text{[A]arithmetic}

\newline

\text{[B]geometric}

\newline

\text{[C]both}

\newline

\text{[D]neither}

Sequence Type Determination: To determine the type of sequence, we need to examine the relationship between consecutive terms. $\newline$ Let's check if it's an arithmetic sequence by finding the difference between consecutive terms. $\newline$ Difference between second and first term: $10 - 2 = 8$ $\newline$ Difference between third and second term: $50 - 10 = 40$ $\newline$ Difference between fourth and third term: $250 - 50 = 200$
Arithmetic Sequence Analysis: Since the differences between consecutive terms are not constant $8, 40, 200$ , the sequence is not arithmetic.
Geometric Sequence Analysis: Now let's check if it's a geometric sequence by finding the ratio between consecutive terms. $\newline$ Ratio of second to first term: $\frac{10}{2} = 5$ $\newline$ Ratio of third to second term: $\frac{50}{10} = 5$ $\newline$ Ratio of fourth to third term: $\frac{250}{50} = 5$
Geometric Sequence Analysis: Now let's check if it's a geometric sequence by finding the ratio between consecutive terms. $\newline$ Ratio of second to first term: $\frac{10}{2} = 5$ $\newline$ Ratio of third to second term: $\frac{50}{10} = 5$ $\newline$ Ratio of fourth to third term: $\frac{250}{50} = 5$ Since the ratio between consecutive terms is constant ( $5$ ), the sequence is a geometric sequence.