What kind of sequence is this? 1, 7, 49, 343, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Identify given sequence: Identify the given sequence. The given sequence is 1, 7, 49, 343, ...Check arithmetic: Check if the sequence is arithmetic by finding the difference between consecutive terms. 7 - 1 = 6 49 - 7 = 42 343 - 49 = 294 The differences are not the same, so the sequence is not arithmetic.Check geometric: Check if the sequence is geometric by finding the ratio between consecutive terms. 7 / 1 = 7 49 / 7 = 7 343 / 49 = 7 The ratios are the same, so the sequence is geometric.Determine sequence type: Determine the type of sequence based on the findings from steps 2 and 3. Since the sequence has a common ratio but not a common difference, it is a geometric sequence.

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What kind of sequence is this? $\newline$ $1, 7, 49, 343, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Math Problems

Algebra 1

Identify arithmetic and geometric sequences

Full solution

Q. What kind of sequence is this?

\newline

1, 7, 49, 343, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Identify given sequence: Identify the given sequence. $\newline$ The given sequence is $1, 7, 49, 343, \ldots$
Check arithmetic: Check if the sequence is arithmetic by finding the difference between consecutive terms. $\newline$ $7 - 1 = 6$ $\newline$ $49 - 7 = 42$ $\newline$ $343 - 49 = 294$ $\newline$ The differences are not the same, so the sequence is not arithmetic.
Check geometric: Check if the sequence is geometric by finding the ratio between consecutive terms. $\newline$ $\frac{7}{1} = 7$ $\newline$ $\frac{49}{7} = 7$ $\newline$ $\frac{343}{49} = 7$ $\newline$ The ratios are the same, so the sequence is geometric.
Determine sequence type: Determine the type of sequence based on the findings from steps $2$ and $3$ . Since the sequence has a common ratio but not a common difference, it is a geometric sequence.