Mathematics
Grade10
Easy

Question

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

  1. 0
  2. 1
  3. -1
  4. 2

Hint:

The given question is about arithmetic progression. Arithmetic progression is a sequence of numbers where, the difference between two consecutive terms is constant. We are given the sequence a, b, c, d, e. We have to find the value of the equation formed by the terms of the given sequence. We will use the concept of common difference to solve the question.

The correct answer is: 0


    The given sequence is a, b, c, d, e.
    The given equation is a – 4b + 6c -4d + c
    The 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 + x
    c = b + x
    = a + x + x
    = a + 2x
    Similarly,
    d = a + 3x
    e = a + 4x
    We 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)
    = 0
    So, the value of given expression is zero.

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

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