What kind of sequence is this? 5, 20, 80, 320, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Examine Differences: To determine the type of sequence, we need to examine the relationship between consecutive terms. Let's start by looking at the difference between terms to see if it's an arithmetic sequence. Difference between second and first term: 20 - 5 = 15 Difference between third and second term: 80 - 20 = 60 Difference between fourth and third term: 320 - 80 = 240Check for Arithmetic Sequence: Now let's check if the differences are the same, which would indicate an arithmetic sequence. First difference: 15 Second difference: 60 Third difference: 240 Since the differences are not the same, this is not an arithmetic sequence.Check for Geometric Sequence: Next, let's check if there is a common ratio between terms, which would indicate a geometric sequence. Ratio of second to first term: 20 / 5 = 4 Ratio of third to second term: 80 / 20 = 4 Ratio of fourth to third term: 320 / 80 = 4Since the ratio between consecutive terms is the same, this is a geometric sequence with a common ratio of 4.

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Math Problems

Grade 8

Identify arithmetic and geometric sequences

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Q. What kind of sequence is this?

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5, 20, 80, 320, \dots

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Choices:

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(A) arithmetic

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(B) geometric

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(D) neither

Examine Differences: To determine the type of sequence, we need to examine the relationship between consecutive terms. Let's start by looking at the difference between terms to see if it's an arithmetic sequence. $\newline$ Difference between second and first term: $20 - 5 = 15$ $\newline$ Difference between third and second term: $80 - 20 = 60$ $\newline$ Difference between fourth and third term: $320 - 80 = 240$
Check for Arithmetic Sequence: Now let's check if the differences are the same, which would indicate an arithmetic sequence. $\newline$ First difference: $15$ $\newline$ Second difference: $60$ $\newline$ Third difference: $240$ $\newline$ Since the differences are not the same, this is not an arithmetic sequence.
Check for Geometric Sequence: Next, let's check if there is a common ratio between terms, which would indicate a geometric sequence. $\newline$ Ratio of second to first term: $\frac{20}{5} = 4$ $\newline$ Ratio of third to second term: $\frac{80}{20} = 4$ $\newline$ Ratio of fourth to third term: $\frac{320}{80} = 4$
Check for Geometric Sequence: Next, let's check if there is a common ratio between terms, which would indicate a geometric sequence. $\newline$ Ratio of second to first term: $\frac{20}{5} = 4$ $\newline$ Ratio of third to second term: $\frac{80}{20} = 4$ $\newline$ Ratio of fourth to third term: $\frac{320}{80} = 4$ Since the ratio between consecutive terms is the same, this is a geometric sequence with a common ratio of $4$ .