How many 25's does Peter count on from 237 until he goes past 1000? How do you know?
Answers
Answer: There are 32 times 25's when Peter count on from 237 until he goes past 1000. This problem can be solved using arithmetic progression.
Step-by-step explanation:
To calculate the count of 25's from 237 until peter goes past 1000, we need to understand what does it means?
It means that he count the numbers of interval 25. For example, after 237 he will count 262 i.e. 237+25= 262 and so on.
Thus, we get a sequence as follow:
237, 262, 287,...... which is an A.P. with a common difference, d=25.
Using the formula of A.P
a_n= a+ (n-1)d
Suppose, a_n=1000
1000= 237 + (n-1)*25
Solving the above equation we get
n-1= (1000-237)/25
n-1= 30.52
Since he goes past 1000 which means the last number is greater than 1000, so we need to round 30.52 to the next integer.
So,
n-1= 31
n= 32