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Question: If the numbers \(a , b , c , d , e\) form an A.P., then the value of \(a - 4 b + 6 c - 4 d + e\) i...

If the numbers a,b,c,d,ea , b , c , d , e form an A.P., then the value of a−4b+6c−4d+ea - 4 b + 6 c - 4 d + e is.

A

1

B

2

C

0

D

None of these

Answer

0

Explanation

Solution

Let be the common difference of the A.P. Then,

a−4b+6c−4d+e=a - 4 b + 6 c - 4 d + e =

a−4(a+D)+6(a+2D)−4(a+3D)+(a+4D)=0a - 4 ( a + D ) + 6 ( a + 2 D ) - 4 ( a + 3 D ) + ( a + 4 D ) = 0.