Question

Question 5.

In the third month of a study, a sugar maple tree is 86 inches tall. In the seventh month, the tree is 92 inches tall. Assuming the tree grows at a constant rate every month, what is the rule for the height of the tree during the nth month?

an = 83 + 1.5(n – 1)
an = 83 + 1.5(n + 1)
an = 86 + 2(n – 1)
an = 86 + 2(n + 1)

Answer 1

an= 86 + 2(n+1)

Explanation:

Answer 2

an= 86 + 2(n+1)

Explanation:

The rule for the height of the tree during the nth month can be determined by finding the common difference, d, between consecutive terms in the sequence. To do this, we subtract the height of the tree in the third month from the height of the tree in the seventh month:

92 - 86 = 6

The common difference is 6, so the height of the tree in the nth month can be represented by the equation:

an = a3 + 6(n - 3)

We know that a3 = 86, so we can substitute this value into the equation:

an = 86 + 6(n - 3) = an+ 86 + 2(n+1)

This equation represents the height of the sugar maple tree during the nth month, where n represents the number of months after the third month.