What kind of sequence is this? 43, 47, 51, 55, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: 43, 47, 51, 55, ... Are the consecutive differences in the sequence equal? 47 - 43 = 4, 51 - 47 = 4, 55 - 51 = 4. The consecutive differences in the sequence are equal.Identify Arithmetic Sequence: Since the consecutive differences are equal, this indicates that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a common difference between consecutive terms.Check for Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. 47 / 43 ≈ 1.093, 51 / 47 ≈ 1.085, 55 / 51 ≈ 1.078. The ratios between consecutive terms are not equal.Conclude Sequence Type: Since the sequence does not have a common ratio, it is not a geometric sequence. A geometric sequence is defined by having a common ratio between consecutive terms.Based on the above steps, we can conclude that the sequence is an arithmetic sequence because it has a common difference but not a geometric sequence as it lacks a common ratio.

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Math Problems

Algebra 2

Classify formulas and sequences

Full solution

Q. What kind of sequence is this?

\newline

43

47

51

55

\dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: $43, 47, 51, 55, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $47 - 43 = 4$ , $51 - 47 = 4$ , $55 - 51 = 4$ . $\newline$ The consecutive differences in the sequence are equal.
Identify Arithmetic Sequence: Since the consecutive differences are equal, this indicates that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a common difference between consecutive terms.
Check for Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. $\newline$ $\frac{47}{43} \approx 1.093$ , $\frac{51}{47} \approx 1.085$ , $\frac{55}{51} \approx 1.078$ . $\newline$ The ratios between consecutive terms are not equal.
Conclude Sequence Type: Since the sequence does not have a common ratio, it is not a geometric sequence. A geometric sequence is defined by having a common ratio between consecutive terms.
Conclude Sequence Type: Since the sequence does not have a common ratio, it is not a geometric sequence. A geometric sequence is defined by having a common ratio between consecutive terms.Based on the above steps, we can conclude that the sequence is an arithmetic sequence because it has a common difference but not a geometric sequence as it lacks a common ratio.