How many consecutive natural numbers starting from one should be added to get 300?
Answers
Step-by-step explanation:
Given :-
Consecutive natural numbers
To find :-
How many consecutive natural numbers starting from one should be added to get 300?
Solution :-
Given that
1+2+3....
First term = 1
Common difference = 2-1 = 1
Since the common difference is same throughout the series
They are in AP.
We know that
Sum of first n terms = Sn = (n/2)[2a+(n-1)d]
Sn = 300
(n/2)[2(1)+(n-1)(1)] = 300
=> (n/2)(2+n-1) = 300
=> (n/2)(n+1) = 300
=> (n²+n)/2 = 300
=> n²+n = 2×300
=> n²+n = 600
=> n²+n -600 = 0
=> n²+25n-24n-600 = 0
=> n(n+25)-24(n+25) = 0
=> (n+25)(n-24) = 0
=> n+25 = 0 or n-24 = 0
=> n = -25 or n = 24
n can not be negative.
Therefore, n = 24
Therefore required terms = 24
Answer:-
The number of natural numbers are added to 1 to get 300 is 24.
Check:-
1+2+3+... (24 terms )
Sum of first 24 terms
=> (24/2)[2×1+(24-1)(1)]
=> 12×(2+23)
=> 12×25
=> 300
Verified the given relations in the given problem.
Used formulae:-
Sum of first n terms = Sn = (n/2)[2a+(n-1)d]
- a = first term
- d = Common difference
- n = number of terms
Sorry , the pic is blur ... not my fault -.-
