Sara is trying a new type of game in which she can jump in either the left direction or in the right direction. Also after each
jump the range of her jump increases by 1 unit. ie if starts from 1 in the next jump she has to jump 2 units then 3 units and
so on.
Given the number of jumos as N the range of the first jump to be 1. What will be the minimum distance Sara can be at from
the starting point
Answers
Range of Sara's jump = n (n+1)/2 units
Explanation:
Given: Sara is trying a new type of game in which she can jump in either the left direction or in the right direction. Also after each jump the range of her jump increases by 1 unit. ie if starts from 1 in the next jump, she has to jump 2 units, then 3 units and so on.
Find: Given the number of jumps as N the range of the first jump to be 1, what will be the minimum distance Sara can be at from?
Solution:
Distance of first jump = 1 unit
Distance of second jump = 2 units
Distance of third jump = 3 units
Distance of fourth jump = 4 units
Distance of fifth jump = 5 units
Distance of Nth jump = N units
So, we get the sequence of jumps as follows: 1, 2, 3, 4, 5.... N
The above sequence is an arithmetic progression with starting number 1 and common difference 1.
An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant.
Range of jump at Nth position = Sum of numbers in the sequence = n(n+1)/2 units.
Given : Sara is trying a new type of game in which she can jump in either the left direction or in the right direction.
Also after each jump the range of her jump increases by 1 unit. ie if starts from 1 in the next jump she has to jump 2 units then 3 units and
so on.
Given the number of jumps as N the range of the first jump to be 1.
To Find : What will be the minimum distance Sara can be at from the starting point
Solution:
minimum distance Sara can be at from the starting point = 0 or 1 depending upon value of N
if jumps are 4m - 1 or 4m then 0 other wise 1
for (4m - 1) and 4m jumps total distance = (4m - 1)*2m or 2m(4m + 1) hence even distance so sara can jump half to left and half to right amd making it zero
for other cases total distance = odd hence she will be minimum at a distance of 1
1 jump minimum distance = 1
2 jump 1 left + 2 right = 1 right
3 jump 1 left + 2 left + 3 right = 0
4 jump 1 left + 2 right + 3 right + 4 left = 0
and maximum distance can be N(N+1)/2
Minimum distance from starting point :
Value of N = 4m- 1, 4m then 0
N = 4m -2 , 4m - 3 then 1
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