Mathematics
Easy

Question

# If a , b , c , d, e are in Arithmetic Sequences., then the value of a –  4b + 6c – 4d + e is

## 01-12 Hint:

## The correct answer is: 0

### The given sequence is a, b, c, d, e.The given equation is a – 4b + 6c -4d + cThe difference between two consecutive terms of an arithmetic progression is constant. It is called as common difference. When we add the difference to preceding term, we get the next term.We will use this concept to solve the question.Let the common difference between the terms be x.So,b = a + xc = b + x= a + x + x= a + 2xSimilarly,d = a + 3xe = a + 4xWe will substitute the values of the terms in the given expression.a – 4b + 6c -4d + e = a – 4(a + x) + 6(a + 2x) – 4(a + 3x) + a + 4x= a – 4a – 4x + 6a + 12x – 4a -12x + a + 4x= (a – 4a + 6a – 4a + a) + ( -4x + 12x – 12x + 4x)= 0So, the value of given expression is zero.

For such questions, we should know the concept of common difference.

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