Question

2] The sum 'S' of the first n natural numbers is given by the relation
S =
n(n+1)
2.
2
Find 'n' if the sum is 120.​

Answer 1

Answer:

n = 15

Step-by-step explanation:

Given---> The sum S of the first n natural number is given by

S = n ( n + 1 ) / 2

To find----> Value of n if S = 120

Solution---> ATQ,

S = n ( n + 1 ) / 2

ATQ, S= 120 , n = ?

=> 120 = n ( n + 1 ) / 2

=> 120 × 2 = n ( n + 1 )

=> 240 = n ( n + 1 )

=> 240 = n × n + n

=> 240 = n² + n

=> n² + n - 240 = 0

Factorize it by splitting the middle term , we know that,

240 = 16 × 15 and 16 - 15 = 1 , applying it , we get,

=> n² + ( 16 - 15 )n - 240 = 0

=> n² + 16n - 15n - 240 = 0

=> n ( n + 16 ) - 15 ( n + 16 ) = 0

=> ( n + 16 ) ( n - 15 ) = 0

If, n + 16 = 0

=> n = - 16 ( impossible , because number of terms can't be negative )

If , n - 15 = 0

=> n = 15

#Answerwithquality

#BAL