In an orchard row, there were 4 distinct type of fruit trees between any two pear trees. Find the position of the tenth pear tree considering the row starts with a pear tree.

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Solution

The number of distinct fruit trees between any two pear trees is $4.$
$∴$ The position of $2^{n d}$ pear tree is $1 + 5 = 6^{t h} .$

Here, pear tree is represented by a green bar.

The position of the third pear tree is $1 + 5 \times 2 = 11^{t h} .$

Similiarly, positions of pear trees is:
$1, 6, 11, 16...$
$\Rightarrow$ position of $10^{t h}$ pine tree $= 1 + 5 \times 9 = 46$

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