Given that the sum to n terms is Sn. The terms are all consecutive natural numbers such that each term is lesser than the succeeding term. Sn= 100. How many series are possible?
Given that the sum to n terms is Sn. The terms are all consecutive natural numbers such that each term is lesser than the succeeding term. Sn= 100. How many series are possible?
The correct option is B 2
We are looking for an AP with a common difference of 1 such that the sum is 100, with a variable “n” number of terms
We know that (Average)*(number of terms) = sum of terms
Let us try to represent 100 ( the sum) in this form
100= 100*1 ( this means that with an average of 100, we have a series of 1 term)
100= 50*2 ( this means that we have 2 consecutive terms with an average of 50, adding up to 100. This is not possible)
Take 100= 20*5
(this is a possible combination of consecutive numbers adding up to 100, with middle term 20. The
numbers are 18 19 20 21 22)
Proceeding in the same manner, we get another possibility as 100 = 12.5 * 8
( the middle terms are 12 and 13, even number of terms =8)
The terms are ( 9,10,11,12,13,14,15,16). These are the two series possible
We are looking for an AP with a common difference of 1 such that the sum is 100, with a variable “n” number of terms
We know that (Average)*(number of terms) = sum of terms
Let us try to represent 100 ( the sum) in this form
100= 100*1 ( this means that with an average of 100, we have a series of 1 term)
100= 50*2 ( this means that we have 2 consecutive terms with an average of 50, adding up to 100. This is not possible)
Take 100= 20*5
(this is a possible combination of consecutive numbers adding up to 100, with middle term 20. The
numbers are 18 19 20 21 22)
Proceeding in the same manner, we get another possibility as 100 = 12.5 * 8
( the middle terms are 12 and 13, even number of terms =8)
The terms are ( 9,10,11,12,13,14,15,16). These are the two series possible
