if a,b,c,l,m are in ap thn 2a-b-2c-l+2m=?
Answers
Solution:-
Given:-
- a , b , c , l , m are in A.P.
To Find:-
- 2a - b - 2c - l + 2m = ?
Find:-
Let's understand this question through an Example.
A.P. :- 2 , 4 , 6 , 8 , 10 , 12 ,...........
Here, we can see that every Next term is the sum of First term and of ( n -1) term.
Ex 1:- 10 .
Means n = 4th term
=) a + ( n-1) = a + 3rd term
=) 2 + 8 = 10
Ex 2:- 12
Means n = 5th term
=) a + ( 5-1) = a + 4th term
=) 2 + 10 = 12
From this we Conclude that, The sum of every next term is equal to the Sum of First term and ( n -1)th term.
So, Given A.P.
a , b , c , l , m are in A.P.
- b = 2a
- c = b + a
- l = c + a
- m = l + a
Now, Substituting these value in the Given Equation. we get,
=) 2a - b - 2c - l + 2m
=) 2a - ( 2a) - 2( b +a) - ( c+a) + 2( l +a)
=) 2a - 2a - 2b - 2a - c - a + 2(l) + 2a
=) - 2b - 2a -a - c + 2( c + a) + 2a
=) - 2b - a - c + 2a + 2c
=) -2b + a + (c)
=) -2b + a + b + a
=) 2a - (b)
=) 2a - 2a
=) 0
Hence,
2a - b - 2c - l + 2m = 0.
Answer:-
a + ( n-1)
a + ( n-1) 2 + 8 = 10 5th term
A.P.
b = 2a
b = 2ac = b + a
b = 2ac = b + al = c + a
b = 2ac = b + al = c + am = l + a
( 2a - b - 2c - l + 2m) 2a -)
(2a) - 2( b +a) - ( c+a) + 2( l +a))
(2a - 2a - 2b - 2a - c - a + 2(l) + 2a)
(-2b - 2a -a - c + 2( c + a) + 2a)
( - 2b - a - c + 2a + 2c)
(-2b + a + (c))
(-2b + a + b + a)
( 2a - (b))
(2a - 2a)
Answer =0