43. The first four terms of an arithmetic sequence are shown. Which of the following is an expression for the total number of dots in the nth term of the sequence?
Answer: C
The expression for the total number of dots in the nth term of the sequence is 3n + 4.
The nth term of the arithmetic sequence can be represented by the expression 3n + 4, which captures the linear growth of the sequence based on its common difference and initial term.
A) 10n-3
This option does not correctly represent the arithmetic sequence as it suggests a much steeper growth rate than observed in the first four terms. The sequence's growth is characterized by a common difference of 3, which is not reflected in this expression.
B) 7n+3
While this expression is linear, it implies a different common difference and initial value than those in the arithmetic sequence. The coefficient of n (7) is inconsistent with the common difference of 3 found in the sequence.
C) 3n+4
This expression accurately describes the nth term of the arithmetic sequence. The coefficient of n (3) represents the common difference, and the constant term (4) correctly reflects the initial term when n equals 1, aligning perfectly with the sequence's progression.
D) n+6
This option does not match the common difference of 3 found in the sequence. The expression suggests a slower growth rate and an incorrect initial value, making it an invalid representation of the arithmetic sequence.
Conclusion
The expression 3n + 4 is the only option that correctly encapsulates the characteristics of the arithmetic sequence, reflecting both the common difference and the initial term. All other options either misrepresent the common difference or the initial value, confirming that they are not suitable representations of the sequence.