Question

in a plantation,there are 230 trees in a row. There are at least 3 papaya trees between any 2 rambutan trees. What is the largest possible number of rambutan trees in that row?​

Answer 1

58

Explanation:

The total number of trees in a row that starts and ends with a rambutan tree is ...

4n -3 . . . . for n rambutan trees

So, the number of rambutan trees that there can be in a row of 230 trees is ...

4n -3 ≤ 230

4n ≤ 233

n ≤ 233/4 = 58 1/4

The largest possible number of rambutan trees in a row of 230 trees is 58.

_____

1 rambutan tree: R . . . n=1, tree count = 1

2 rambutan trees: RpppR . . . n=2, tree count = 5

3 rambutan trees: RpppRpppR . . . n=3, tree count = 9

The tree count is an arithmetic sequence with first term 1 and common difference 4. Then the n-th term of the sequence is ...

tn = a1 +d(n -1) = 1 +4(n -1) = 4n -3

Term 58 is ...

t58 = 4·58 -3 = 229

So, the row of trees might be ...

RpppRppp ... RpppRpppRp . . . . with 58 R and 172 p.