The third term of an ap is 4m-2n.if the ninth term is 2m- 8n.find the common difference interms of m and n
Answers
Step-by-step explanation:
Given :-
The third term of an ap is 4m-2n.
The ninth term of the AP is 2m- 8n.
To find :-
Find the common difference in terms of m and n ?
Solution :-
We know that
General term of an AP = an = a+(n-1)d
Where , a is the first term
d is the common difference
n is the number of terms
Given that:
The third term of an AP = a3 = 4m-2n
=> a+(3-1)d = 4m-2n
=>a+2d =4m-2n
=> a = 4m-2n-2d ----------(1)
The ninth term of an AP = a9 = 2m-8n
=> a+(9-1)d = 2m-8n
=> a+8d =2m-8n
=> a = 2m-8n-8d ----------(2)
From (1) &(2)
4m-2n-2d = 2m-8n-8d
=> -2d +8d = 2m-8n-4m+2n
=>6d = (2m-4m)+(-8n+2n)
=> 6d = (-2m)+(-6n)
=> 6d = (-2m-6n)
=> d = (-2m-6n)/6
=> d = 2(-m-3n)/6
=>d = (-m-3n)/3 (or)
=> d = -(m+3n)/3
Therefore , d = -(m+3n)/3
Answer:-
The common difference of the AP in terms of m and n is -(m+3n)/3
Used formulae :-
General term of an AP = an = a+(n-1)d
Where , a is the first term
d is the common difference
n is the number of terms