What kind of sequence is this? $\newline$ $5, 20, 100, 600, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Grade 8

Identify arithmetic and geometric sequences

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Q. What kind of sequence is this?

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5, 20, 100, 600, \dots

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Choices:

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(A) arithmetic

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(B) geometric

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(D) neither

Identify Pattern: To determine the type of sequence, we need to look at the pattern of change from one term to the next. Let's start by examining the differences or ratios between consecutive terms.
Calculate Differences: First, we calculate the difference between the second and the first term: $20 - 5 = 15$ .
Check Arithmetic Sequence: Next, we calculate the difference between the third and the second term: $100 - 20 = 80$ .
Check Geometric Sequence: Now, we calculate the difference between the fourth and the third term: $600 - 100 = 500$ .
Final Conclusion: We notice that the differences between consecutive terms $(15, 80, 500)$ are not constant, so this sequence is not an arithmetic sequence.
Final Conclusion: We notice that the differences between consecutive terms ( $15$ , $80$ , $500$ ) are not constant, so this sequence is not an arithmetic sequence.Let's now check if it's a geometric sequence by finding the ratios of consecutive terms. We divide the second term by the first term: $20 \div 5 = 4$ .
Final Conclusion: We notice that the differences between consecutive terms ( $15$ , $80$ , $500$ ) are not constant, so this sequence is not an arithmetic sequence.Let's now check if it's a geometric sequence by finding the ratios of consecutive terms. We divide the second term by the first term: $20 \div 5 = 4$ .We divide the third term by the second term: $100 \div 20 = 5$ .
Final Conclusion: We notice that the differences between consecutive terms $(15, 80, 500)$ are not constant, so this sequence is not an arithmetic sequence. Let's now check if it's a geometric sequence by finding the ratios of consecutive terms. We divide the second term by the first term: $20 \div 5 = 4$ . We divide the third term by the second term: $100 \div 20 = 5$ . We divide the fourth term by the third term: $600 \div 100 = 6$ .
Final Conclusion: We notice that the differences between consecutive terms $15$ , $80$ , $500$ are not constant, so this sequence is not an arithmetic sequence. Let's now check if it's a geometric sequence by finding the ratios of consecutive terms. We divide the second term by the first term: $20 \div 5 = 4$ . We divide the third term by the second term: $100 \div 20 = 5$ . We divide the fourth term by the third term: $600 \div 100 = 6$ . The ratios between consecutive terms $4$ , $5$ , $6$ are not constant, so this sequence is not a geometric sequence either.
Final Conclusion: We notice that the differences between consecutive terms $(15, 80, 500)$ are not constant, so this sequence is not an arithmetic sequence. Let's now check if it's a geometric sequence by finding the ratios of consecutive terms. We divide the second term by the first term: $20 \div 5 = 4$ . We divide the third term by the second term: $100 \div 20 = 5$ . We divide the fourth term by the third term: $600 \div 100 = 6$ . The ratios between consecutive terms $(4, 5, 6)$ are not constant, so this sequence is not a geometric sequence either. Since the sequence is neither arithmetic (differences are not constant) nor geometric (ratios are not constant), the correct choice is $(D)$ neither.