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?

Rationale

3n + 4 represents the total number of dots in the nth term of the arithmetic sequence.

In an arithmetic sequence, each term can be expressed as a linear function of its position. Given that the first term is 4 and the common difference is 3, the nth term can be calculated using the expression 3n + 4.

A (10n-3) YOUR ANSWER

This expression suggests a linear growth rate of 10 per term, which does not match the common difference of the sequence. The initial term of this expression, when n = 1, would yield 7, which is inconsistent with the first term of the sequence provided.

B (7n+3) YOUR ANSWER

While this expression has a linear format, the common difference implied by this formula is 7, resulting in incorrect term values. The first term calculated with n = 1 would be 10, which does not align with the actual first term of 4.

D (n+6) YOUR ANSWER

This expression has a growth rate of 1 per term, which is far too slow given that the common difference in the sequence is 3. The first term calculated would yield 7 when n = 1, which again does not correspond with the sequence's initial term.

Conclusion

The correct expression for the nth term of the arithmetic sequence is 3n + 4, reflecting both the common difference and the initial term accurately. The other options fail to represent the sequence's structure, either by incorrect initial values or growth rates, hence confirming 3n + 4 as the valid expression for the total number of dots in the nth term.

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?

3n + 4 represents the total number of dots in the nth term of the arithmetic sequence.

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