Question

The first four terms of a sequence are shown below. Which of the following functions expresses the number of small squares in the nth term of the sequence?

A) n^2 + n
B) 2n^2 + n
C) 3n + 2
D) n^3 - n

Answer 1

The function that expresses the number of small squares in the nth term of the sequence provided is B) 2n^2 + n. This is determined by pairing terms to simplify the expression in the sequence down to 2n^2.

Step-by-step explanation:

The student's question is looking for a function that expresses the number of small squares in the nth term of the given sequence. To find the pattern, we can use the information provided about manipulating terms within the sequence.

We are given instructions to consider the sum as if we were grouping terms in pairs that sum to 2n. By doing so, the sum for each term always results in a pair of n terms adding up to 2n. This is further simplified to 2n2, indicating that each term in the sequence equals the square of the number of terms multiplied by two.

Therefore, the function that expresses the number of small squares in the nth term of the sequence is B) 2n2 + n.