Question

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​

Answer 1

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.

Answer 2

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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