Question

If a father planted trees equal to the cubes ages of his son's birthday from his son's 10th birthday to 20th birthday how many trees would he plant at the end of his 20th Birthday​

Answer 1

Given :

father planted trees equal to the cubes ages of his son's birthday

The trees planted from 10th birthday to 20th birthday

To Find :

The number of  trees would planted at the end of his 20th Birthday​

Solution :

As trees are planted as age cubes So, There are in cubes of first n natural numbers

We know , sum of cubes of first n natural numbers  =  [$\dfrac{ n ( n + 1 ) }{2}$]²

statement 1

For 10th birthdays

Put n = 10

So, The trees planted as cubes =  [$\dfrac{ 10 ( 10 + 1 ) }{2}$]²

                                                    = [$\dfrac{ 10 ( 11 ) }{2}$]²

                                                    = 55 × 55 = 3025

Statement II

For 20th birthdays

Put n = 20

So, The trees planted as cubes =  [$\dfrac{ 20 ( 20 + 1 ) }{2}$]²

                                                    = [$\dfrac{ 20 ( 21 ) }{2}$]²

                                                    = 210 × 210 = 44100

Now,

Number of the trees planted between birthday = Trees at 20th birthdays - Trees at 10th birthdays

i.e   Number of the trees planted between birthday = 44100 - 3025

                                                                                     = 41075

Hence, The  Number of the trees planted at the end of 20th birthday is 41075   Answer