There are m multiples of 6 in range [0, 100] and n multiples of 6 in [-6, 35]. Find out the value of X, if X = m - n. Where X, m, and n are positive integer.
Answers
Answer:
10
Step-by-step explanation:
Using the indentities of AP:
xth term = a + (x - 1)d, a is the first term and d is the common difference.
For m:
First no. divisible by 6 is 6 and last term is 96, in [0, 100].
First term = 0, mth term = 96, d = 6.
=> mth term = a + (m - 1)d
=> 96 = 0 + (m - 1)(6)
=> 17 = m
For n:
First no. divisible by 6 is -6 and last term is 30, in [-6, 35].
First term = -6, nth term = 30, d = 6.
=> nth term = a + (n - 1)d
=> 30 = -6 + (n - 1)(6)
=> 7 = n
Therefore,
X = m - n => X = 17 - 7
X = 10
If you're not familiar to AP:
If you start with 6, you would stop at 96, if you keep on adding 6 till 100(from 0).
You get: terms = 17
m = 17
Similarly, if you start from -6 and keep on adding 6 till 35, you get n = 7.
Hence, X = 17 - 7 = 10
Answer:
Given :-
- There are m multiple of 6 in range of [0, 100] and n multiple of 6 in [- 6, 35].
- m and n are positive integers.
To Find :-
- What is the value of X, if X = m - n.
Solution :-
Given :
- First term (a) = 0
- mth term of an AP () = 96
- Common difference (d) = 6
As we know that,
nth term of an AP Formula :
where,
- = nth term of an AP
- a = First term of an AP
- n = Number of terms
- d = Common difference
Similarly,
mth term of an AP Formula :
where,
- = mth term of an AP
- a = First term of an AP
- m = Number of terms
- d = Common difference
According to the question by using the formula we get,
Given :
- First term (a) = - 6
- nth term of an AP () = 30
- Common difference (d) = 6
So, for nth term we know that :
where,
- = nth term of an AP
- a = First term of an AP
- n = Number of terms
- d = Common difference
According to the question by using the formula we get,
Hence, the value of X will be :
We have :
Then, the value of X is :
The value of X is 10.