What kind of sequence is this? 1, 8, 64, 512, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Determine Sequence Type: To determine the type of sequence, we need to examine the relationship between consecutive terms.Check Arithmetic Sequence: First, let's check if it's an arithmetic sequence by finding the difference between consecutive terms. 8 - 1 = 7 64 - 8 = 56 512 - 64 = 448 The differences are not constant, so it is not an arithmetic sequence.Check Geometric Sequence: Now, let's check if it's a geometric sequence by finding the ratio between consecutive terms. 8 ÷ 1 = 8 64 ÷ 8 = 8 512 ÷ 64 = 8 The ratio is constant, so it is a geometric sequence.

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What kind of sequence is this? $\newline$ $1, 8, 64, 512, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Math Problems

Grade 8

Identify arithmetic and geometric sequences

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Q. What kind of sequence is this?

\newline

1, 8, 64, 512, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Determine Sequence Type: To determine the type of sequence, we need to examine the relationship between consecutive terms.
Check Arithmetic Sequence: First, let's check if it's an arithmetic sequence by finding the difference between consecutive terms. $\newline$ $8 - 1 = 7$ $\newline$ $64 - 8 = 56$ $\newline$ $512 - 64 = 448$ $\newline$ The differences are not constant, so it is not an arithmetic sequence.
Check Geometric Sequence: Now, let's check if it's a geometric sequence by finding the ratio between consecutive terms. $\newline$ $8 \div 1 = 8$ $\newline$ $64 \div 8 = 8$ $\newline$ $512 \div 64 = 8$ $\newline$ The ratio is constant, so it is a geometric sequence.