Q3 of 239 Page 54

A vendor arranged his apples as in the following pattern:

A. If there are ten rows of apples, can you find the total number of apples without actually counting?


B. If there are twenty rows, how many apples will be there in all?



Can you recognize a pattern for the total number of apples? Fill this chart and try!


Given in the pattern of apples arranged,


1st row = 1 apple, 2nd row = 2 apples, 3rd row = 3 apples and 4th row = 4 apples and so on.


So, this can be expressed as 1 + 2 + 3 + 4 + …


We know that sum of numbers from 1 to n is .


A. We have to find the total number of apples in 10 rows.


Here n = 10.


∴ Number of apples in 10 rows = = = 55 apples


B. We have to find the total number of apples in 20 rows.


Here n = 20.


∴ Number of apples in 20 rows = = = 210 apples


Here, the series starts with 1 and the sum of every subsequent term is the sum of previous two. (Fibonacci series)



More from this chapter

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1

Complete the following patterns:

1, 3, 6, 10, ___, ___, ___.

 1

Complete the following patterns:

1, 1, 2, 3, 5, 8, 13, 21, ___, ___, ___


(This sequence is called FIBONACCI SEQUENCE)

 1

Complete the following patterns:

1, 8, 27, 64, ___, ___, ___.

 2

A water tank has steps inside it. A monkey is sitting on the top most step. (ie, the first step) The water level is at the ninth step.

A. He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?



B. After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down in every move. In how many jumps will he reach back the top step?