if a father planted trees equal to the cubes of 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
Answers
Given:
A father planted trees equal to the cubes of ages of his son's birthday from his son's 10th birthday to 20th birthday.
To Find:
how many trees would he plant at the end of his 20th birthday.
Solution:
1) Father planted the cube of the age of his son so here the concept of the sum of the cube of the natural number is used.
2) It is given in the question that the father planted the tree from his 10th birthday to 20th birthday.
3) So here will subtract the sum of 10 from the sum of the 20
4) We know that sum of cubes of first n natural numbers is = (n(n+1)/2)².
5) number of the tree given by:
Case 1:
- For 20 birthdays (n=20)
- (n(n+1)/2)²
- (20 × 21 / 2)²
- (210)²
- 44100
Case 2:
- For 10 birthdays (n =10)
- (n(n+1)/2)²
- (10× 11 /2)²
- (55)²
- 3025
6) Number of the trees is = 20 birthdays - 10 birthdays
= 44100 - 3025
= 41075.