Four numbers are inserted between the numbers 4 and 39 such that an AP. results. Find the biggest of these four numbers.

Given: Four numbers are inserted between the numbers $4$ and $39$ such that an AP. results. 

To do: To find the biggest of these four numbers.

When $n$ numbers are inserted between two numbers $a$ and $b$, then the common difference $d$ is given by, $d=\frac{b-a}{n+1}$

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Here, $b=39,\ n=4$ and $a=4$

 

$\Rightarrow d=\frac{39-4}{4+1}$

$\Rightarrow d=\frac{35}{5}$

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$\Rightarrow d=7$

Therefore the inserted numbers betwween $4$ and $39$ are: $11,\ 18,\ 25,\ 32$

The largest number is $32$.