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Complete the problems below.

Your school is sponsoring a tree planting project at a local national forest. There are 10 rows of trees that need to be planted by volunteers: 6 trees in the 1st row, 11 trees in the 2nd row, 16 trees in the 3rd row, and so on.

1. How many trees are in the 9th row of the tree-planting project?

The figures below represent the first 3 rows. The sequence [tex]\(\{6, 11, 16, \ldots\}\)[/tex] is generated by the function [tex]\(f(n) = 5n + 1\)[/tex], where [tex]\(n\)[/tex] is the row number and [tex]\(f(n)\)[/tex] is the number of trees in the row.



Answer :

GinnyAnswer
Certainly! Let's take the given information step-by-step:

1. We are given a tree planting project with a specific pattern for the number of trees in each row.
2. The number of trees in each row follows a specific sequence such that:
- The 1st row has 6 trees.
- The 2nd row has 11 trees.
- The 3rd row has 16 trees.
- And so on.

3. We are provided with a sequence function [tex]\( f(n) = 5n + 1 \)[/tex], where [tex]\( n \)[/tex] is the row number, and [tex]\( f(n) \)[/tex] is the number of trees in that row.

4. To determine the number of trees in the 9th row, we substitute [tex]\( n = 9 \)[/tex] into the sequence function.

So let's follow these steps:

1. Substitute [tex]\( n = 9 \)[/tex] into the function [tex]\( f(n) = 5n + 1 \)[/tex]:
[tex]\[ f(9) = 5 \times 9 + 1 \][/tex]

2. Calculate the result inside the function:
[tex]\[ 5 \times 9 = 45 \][/tex]

3. Add 1 to the result:
[tex]\[ 45 + 1 = 46 \][/tex]

Therefore, according to our sequence function, the 9th row will have [tex]\( 46 \)[/tex] trees.

So, the number of trees in the 9th row of the tree-planting project is [tex]\( 46 \)[/tex].

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